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.

A Study of Dynamic Analysis Method for the Rigid-Flexible Coupled Bar Linkage System

In order to present a dynamic analysis method for the rigid-flexible coupled bar linkage system(RFCBLS),the flexible element motion equation was gotten by Lagrange Equation and the rigid element motion equation was gotten based on rigid constraint conditions.The multi-body system(MBS) is a complex mechanism and its components have quite different rigidities.If it is considered as a rigid MBS(RMBS) to do its dynamic analysis,elastic deformation's ignorance will lead to inaccurate analysis.If it is considered as a flexible MBS(FMBS) to establish,analyze,and solve the model,quite large system equations make it difficult to solve.The better method is as follows:the complex mechanism system is regarded as a rigid-flexible coupled system(RFCS) to make dynamic characteristic of rigid components be equivalent,system equation is established by FMBS' way,and system equation dimensions are reduced by transition matrices' introduction.A dynamic analysis method for rigid element and flexible element coupling was presented based on the FMBS.The analyzed crank slide-block mechanism results show that the dynamic analysis method for RFCBLS is quick and convenient.

A DYNAMIC MODEL FOR ROCKET LAUNCHER WITHCOUPLED RIGID AND FLEXIBLE MOTION

The dynamics of a coupled rigid-flexible rocket launcher is reported. The coupled rigid-flexible rocket launcher is divided into two subsystems, one is a system of rigid bodies, the other a flexible launch tube which can undergo large overall motions spatially. First, the mathematical models for these two subsystems were established respectively. Then the dynamic model for the whole system was obtained by considering the coupling effect between these two subsystems. The approach, which divides a complex system into several simple subsystems first and then obtains the dynamic model for the whole system via combining the existing dynamic models for simple subsystems, can make the modeling procedure efficient and convenient.

Dynamic analysis of spatial parallel manipulator with rigid and flexible couplings

The dynamics of spatial parallel manipulator with rigid and flexible links is explored. Firstly, a spatial beam element model for finite element analysis is established. Then, the differential equation of motion of beam element is derived based on finite element method. The kinematic constraints of parallel manipulator with rigid and flexible links are obtained by analyzing the motive parameters of moving platform and the relationships of movements of kinematic chains, and the overall kinetic equation of the parallel mechanism with rigid and flexible links is derived by assembling the differential equations of motion of components. On the basis of abovementioned analyses, the dynamic mechanical analysis of the spatial parallel manipulator with rigid and flexible links is conducted. After obtaining the method for force analysis and expressions for the calculation of dynamic stress of flexible components, the dynamic analysis and simulation of spatial parallel manipulator with rigid and flexible links is performed. The result shows that because of the elastic deformation of flexible components in the parallel mechanism with rigid and flexible links, the force on each component in the mechanism fluctuates sharply, and the change of normal stress at the root of drive components is also remarkable. This study provides references for further studies on the dynamic characteristics of parallel mechanisms with rigid and flexible links and for the optimization of the design of the mechanism.

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.

Dynamic Study on Rigid and Flexible Coupling System for Terminally Sensitive Submunition

A kinetic model of the rigid and flexible coupling system for terminally sensitive submunition is set up with Kane's method. The parachute is considered as a flexible body, the flexible displacement is expressed with modal spread method, the position of the parachute is expressed with a hybrid coordinate method, and the kinematics of the terminally sensitive submunition is analyzed. Ten generalized coordinates relative to the attitude of the terminally sensitive submunition are chosen, and the correlative generalized active forces, the generalized inertial forces, the generalized internal forces are calculated in turn. On the base of the Kane's method, the ten degrees of freedom dynamic equations for the coupled terminally sensitive submunition are finally set up. This model can be used to expediently simulate and analyze accurately the exterior ballistic trajectory of terminally sensitive submunition, and provide the overall design of the terminally sensitive submunition with some helpful references.

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 sys- tem, the dynamic equations of the rigid flexible coupling system with dynamic stiffening are estab- lished. 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 po- sition is incorporated into the continuous dynamic equations of the system by use of the Dirac lunch tion and the Heaviside function. Then, based on the conclusions of orthogonalization about the nor- mal 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-or- der model established in this paper, which indicates the dynamic responses of the rigid flexible cou- pling system with large overall motion accurately. The results also show that the mass has a soften- ing 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.

MODELING AND ANALYSIS OF A COUPLED RIGID_FLEXIBLE SYSTEM

Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of failing to account for the effects of dynamic stiffening, conventional methods based on the linear theories can lead to erroneous results in many practical applications. In this paper, the idea of 'centrifugal potential field', which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established. Based on this equation, first it is proved that the elastic motion of the system has periodic property, then by using Frobenius' method its exact solution is obtained. The influences of large overall rigid motion on the elastic vibration mode shape and frequency are analysed through the numerical examples.

Dynamic response analysis of a moored crane-ship with a flexible boom

The dynamic response of moored crane-ship is studied. Governing equations for the dynamic response of a crane-ship coupled with the pendulum motion of the payload are derived based on Lagrange’s equations. The boom is modeled based on finite element method, while the payload is modeled as a planar pendulum of point mass. The dynamic response was studied using numerical method. The calculation results show that the large-amplitude responses occur at wave periods near the natural period of the payload. Load swing angle is smaller for crane-ship with flexible boom, in comparison with rigid boom. The ship surge mo- tions have large vibrations for crane-ship with flexible boom, which were not observed for a rigid boom. The analysis identifies the significance of key parameters and reveals how the system design can be adjusted to avoid critical conditions.

A node-based smoothed point interpolation method for dynamic analysis of rotating flexible beams

We proposed a mesh-free method, the called node-based smoothed point interpolation method(NS-PIM),for dynamic analysis of rotating beams. A gradient smoothing technique is used, and the requirements on the consistence of the displacement functions are further weakened. In static problems, the beams with three types of boundary conditions are analyzed, and the results are compared with the exact solution, which shows the effectiveness of this method and can provide an upper bound solution for the deflection.This means that the NS-PIM makes the system soften. The NS-PIM is then further extended for solving a rigid-flexible coupled system dynamics problem, considering a rotating flexible cantilever beam. In this case, the rotating flexible cantilever beam considers not only the transverse deformations,but also the longitudinal deformations. The rigid-flexible coupled dynamic equations of the system are derived via employing Lagrange’s equations of the second type. Simulation results of the NS-PIM are compared with those obtained using finite element method(FEM) and assumed mode method. It is found that compared with FEM, the NS-PIM has anti-ill solving ability under the same calculation conditions.

Impacts of flexible obstructive working environment on dynamic performances of inspection robot for power transmission line

The rigid-flexible coupling dynamic modeling and simulation of an inspection robot were conducted to study the influences of the flexible obstructive working environment i.e. overhead transmission line on the robot’s dynamic performance. First, considering the structure of the obstacles and symmetrical mechanism of the robot prototype, four basic subactions were abstracted to fulfill full-path kinematic tasks. Then, a multi-rigid-body dynamic model of the robot was built with Lagrange equation, while a multi-flexible-body dynamic model of a span of line was obtained by combining finite element method (FEM), modal synthesis method and Lagrange equation. The two subsystem models were coupled under rolling along no-obstacle segment and overcoming obstacle poses, and these simulations of three subactions along different spans of line were performed in ADMAS. The simulation results, including the coupling vibration parameters and driving moment of joint motors, show the dynamic performances of the robot along flexibile obstructive working path: in flexible obstructive working environment, the robot can fulfill the preset motion goals; it responses slower in more flexible path; the fluctuation of robot as well as driving moment of the corresponding joint in startup and brake region is greater than that in rigid environment; the fluctuation amplitude increases with increasing working environment flexibility.

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 subsystemmodeling 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 beamand 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 beamand the central rigid body are established via structural dynamics and angular momentumtheory 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 showthat： 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.

考虑磨损演化的铰链式襟翼机构动力学仿真研究

不同卡位的襟翼气动载荷差别很大,使得轴承在不同襟翼偏角下所承受载荷也存在明显差异,这导致在不同角度位置的轴承磨损深度不一致。因此,引入均匀磨损深度的方法难以适用于襟翼的动力学特性分析。为解决这一问题,提出了一种基于最小二乘法的动力学建模方法。根据襟翼翼面的连接特点利用C-B法对其进行柔性化,并采用RBE2单元建立刚柔耦合动力学模型。联合UAMP、DISP、UMESHMOTION子程序进行磨损演化仿真,获取铰链轴承的非均匀磨损数据,同时通过最小二乘拟合建立磨损深度和襟翼偏角角度以及摩擦因数的映射关系。将该映射关系以铰链轴承中心点的偏移量和轴承摩擦因数的方式更新刚柔耦合动力学模型,以获取在磨损影响下的襟翼机构动力学响应,验证了方法的适用性和有效性。结果表明,随着磨损的进行,襟翼内外侧轴承转轴同轴度逐渐降低,内外侧驱动力矩随之增加,增加幅度最大为15.08%。该方法可为襟翼机构的设计及轴承选型提供一定支持。

多簧片结构的磁保持继电器多物理场刚柔耦合仿真模型建立和实验分析

多簧片结构的磁保持继电器衔铁转动引起的触点碰撞、弹跳现象使运动过程复杂,静、动态特性理论分析和仿真模型建立困难。以某型号多簧片结构的磁保持继电器为研究对象,理论分析结构拓扑及工作机理,考虑触点间切入深度,引入狄拉克函数和赫维赛德函数,解决簧片受力分散及触点由于碰撞、弹跳引起的作用力不连续问题;将簧片等效为悬臂梁,基于欧拉-伯努利梁理论建立触簧系统三簧片分段耦合动力学模型。利用Ansys Maxwell引入基于误差的自适应网格划分方法求解电磁机构静态特性;考虑触簧系统簧片运动变形效应,通过ADAMS基于模态理论,构建刚柔耦合动力学仿真模型。基于分段动力学思想,搭建电-磁-机械运动多物理场刚柔耦合仿真模型。利用高速摄像机、电流探头等设计磁保持继电器实验方案,搭建实验平台,测试并分析磁保持继电器触点吸合运动时间、触点压力、弹跳时间、线圈电流,并分析人工装配簧片引起触点压力不同使继电器动作过程存在的不一致性问题,验证该文所提多簧片结构的磁保持继电器特性分段耦合分析方法和多物理场刚柔耦合仿真模型的有效性。

深水隔水管-防喷器组耦合系统动力学建模与仿真验证

在深水钻井过程中,隔水管与防喷器组系统是整个作业环节的重要一环。由于在作业过程中面临着诸多风险,因此,建立精确的隔水管-防喷器组耦合系统力学分析模型,准确分析其力学行为和性能,对指导钻井作业安全进行具有重要意义。目前大多只关注于对隔水管的独立建模而忽视防喷器组的潜在影响,这将导致所建模型与实际情况存在差异,使得隔水管系统的力学特性无法得到精确分析。提出了隔水管与防喷器组刚柔耦合概念,推导耦合系统动能、势能,采用拉格朗日方法建立理论模型,用Newmark-β直接积分法对动力学模型进行数值计算。采用ADAMS软件进行了仿真建模,开展不同工况条件下的动态响应对比分析。结果表明,理论模型得到的隔水管横向位移包络线、弯矩包络线、隔水管中部节点横向位移时程曲线和底部弯矩时程曲线与ADAMS仿真结果吻合良好,从而表明了该理论模型的重要性,可为我国隔水管的设计和分析提供参考和支持。

大跨度高速铁路桥梁端伸缩装置区段车轨动力响应

为了确保大跨度高速铁路桥梁端伸缩装置区段列车安全运营,通过建立梁端伸缩装置区段车辆-轨道刚柔耦合模型,研究了不同伸缩量、不同车辆行驶速度下梁端伸缩装置各部件动力响应变化规律,并对随机不平顺激励叠加梁端刚度不平顺下车辆运行安全性进行评估。结果表明:梁端伸缩装置各部件动力响应整体随车速增加而呈增大趋势,且各部件垂向加速度随车速变化较大;不同伸缩量下梁端伸缩装置区域钢轨及可动钢枕动力响应整体随梁缝扩大而呈增大趋势,且可动钢枕垂向位移及伸缩装置各部件垂向加速度随伸缩量变化较大;施加随机不平顺后,轮重减载率在车速420 km/h时出现超限情况,钢轨垂向位移在拉伸300~500 mm状态、车速330 km/h时出现超限情况。

织物衬垫磨损对自润滑关节轴承动力学的影响

自润滑关节轴承在服役过程中,衬垫的磨损导致自润滑关节轴承内外圈之间产生间隙,自润滑运动副间隙的存在加速了内外圈之间的碰撞以及衬垫的进一步磨损,对自润滑关节轴承的动力学特性产生较大的影响。此外,衬垫的磨损还会导致各构件非线性特性的恶化,降低自润滑关节轴承的稳定性。为研究织物衬垫磨损对自润滑关节轴承动力学响应的影响,文中建立了带间隙的自润滑关节轴承运动副矢量模型。首先,通过修正Lankarani-Nikravesh(L-N)法向接触力模型和改进的库仑摩擦力模型,对内外圈间隙处的碰撞力进行建模;然后,基于牛顿第二定律建立了含间隙的刚柔耦合动力学方程;最后,分析讨论不同织物衬垫磨损量和不同摩擦因数条件下含间隙的自润滑关节轴承传动系统的动力学特性,并利用相图和Poincare映射图分析了自润滑关节轴承的非线性特性。结果表明:随着织物衬垫磨损量的增加,自润滑关节轴承内圈和外圈的动力学行为表现出非线性特性;衬垫磨损量一定时,随着衬垫摩擦因数的增加,系统稳定性得到提高,抑制了混沌现象的发生。

细长桁架臂卸载反弹动应力分布规律及试验

为研究细长桁架臂在卸载冲击下的动态响应变化规律,提出了基于等效梁振型函数的桁架臂动应力分布计算模型。根据等效梁振型函数,探讨了卸载后桁架臂动应力分布假设,分析了影响桁架臂卸载反弹动响应的相关参数。以装备细长桁架臂的动臂塔机为对象,建立了桁架臂精细化有限元模型和起重机刚柔耦合模型,通过仿真辨识了应力分布模型的关键参数。实施了动臂塔机系列载荷卸载冲击试验,桁架臂上主弦杆的动应力试验值与理论计算结果误差小于7%,表明动应力分布理论模型与实际相符。通过理论模型预测了极限工况下桁架臂上主弦杆动应力分布状态,发现在最大载荷卸载条件下起重臂动应力峰值超过结构承载极限,为卸载条件下起重机关键结构的优化设计提供依据。

Rigid-flexible coupling dynamic modeling and vibration control for flexible spacecraft based on its global analytical modes

In this study, we used global analytical modeswfny(GAMs) to develop a rigid-flexible dynamic modeling approach for spacecraft with large flexible appendages(SwLFA). This approach enables the convenient and precise calculation of the natural characteristics for designing an attitude control law for the spacecraft while simultaneously suppressing the active vibration of its flexible appendages. We simplify the flexible spacecraft as a rigid-flexible coupling hub-beam system with tip mass and derive the system's governing equations of motion based on Hamilton's principle. By solving the linearized form of those equations with their associated boundary conditions, we obtain the frequencies as well as the corresponding GAMs of flexible spacecraft,which we use to discretize the equations of motion. Using this approach, we performed numerical simulations to investigate the system's global modes and assess the performance of the controller based on the GAM model. The results reveal that the GAM model can be used to directly calculate the exact global modes of SwLFAs and that the controller based on the discrete GAM model can achieve a control-index for a SwLFA in a shorter time with less input energy than other methods.

中低速磁浮圆曲线钢箱梁桥车致振动响应研究

随着圆曲线钢箱梁桥在城市交通中的应用愈发广泛,为探究其在中低速磁浮车辆运行作用下的振动响应特性,基于多体动力学和有限元方法建立车辆-轨道-钢箱梁刚柔耦合动力学模型,采用动态电磁阻尼力影响的二维磁轨关系,并考虑轨道关键部件的参振作用,分析圆曲线段钢箱梁的振动特性,探讨钢箱梁板厚、车辆速度及车体质量对钢箱梁振动响应的影响。结果表明:受曲率影响,钢箱梁在发生弯曲的同时亦会伴生扭转,产生弯扭耦合振动;钢箱梁的振动主要由10~20 Hz的钢箱梁整体弯曲振动、30~40 Hz的钢箱梁扭转振动以及50~70 Hz的轨道局部振动引起;计算得到的钢箱梁跨中横向及垂向最大挠度分别为1.26 mm、3.88 mm,均满足相关标准要求,钢箱梁具有足够的支撑刚度;各工况下的垂向加速度均未超过5.0 m/s^(2)的限值,且最高达到2.2 m/s^(2);在板厚10 mm以及超员载荷工况下,横向加速度大多超过1.4 m/s^(2)的限值,且最高达到4.0 m/s^(2);车辆速度的减小和车体质量的增加均会放大弯扭耦合作用影响,而板厚的增加则能够有效降低弯扭耦合作用影响,当板厚由10 mm增至40 mm时,一阶横弯及扭转频率对应振幅分别减小94.3%、98.7%。