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.

Ride comfort evaluation for road vehicle based on rigid-flexible coupling multibody dynamics

In the present research two different whole vehicle multibody models are established respectively, including rigid and rigid-flexible coupling multibody vehicle models. The former is all composed by rigid bodies while in the later model, the flexible rear suspension is built based on the finite element method （FEM） and mode superposition method, in which the deformations of the components are considered. The ride simulations with different speeds are carried out on a 3D digitalized road, and the weighted root mean square （RMS） of accelerations on the seat surface,backrest and at the feet are calculated. The comparison between the responses of the rigid and rigid-flexible coupling multibody models shows that the flexibility of the vehicle parts significantly affects the accelerations at each position, and it is necessary to take the flexibility effects into account for the assessment of ride comfort. C 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi： 10.1063/2.1301304]

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 Simulation for Rigid-Flexible Coupling Model of Gear Transmission System Based on ADAMS

The influence of the flexible body for the motion of gear transmission system is analyzed and the foundation for a more accurate assessment of gear transmission system is established when it has battle damage faults. By using Pro / E software,the virtual prototype model of gear transmission system in the speed reducer is established,and the rigid model and rigid-flexible coupling model are simulated respectively in ADAMS to obtain the data of gear meshing force. It can be concluded that rigid-flexible coupling model can reflect the real motion better than rigid model by comparing the simulation data of two models.

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.

Nonlinear dynamic analysis on rigid-flexible coupling system of an elastic beam

Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations to an elastic beam with free large overall motion. Based on initial stress method, the nonlinear coupling equations of elastic beams are obtained with free large overall motion and the attached stiffness matrix is derived by solving sub-static formulation. The angular velocity and the tip deformation of the elastic pendulum are calculated. The analytical results show that the simulation results of the present model are tabled and coincide with the one-order approximate model. It is shown that the simulation results accord with energy conservation principle.

Geometric nonlinear formulation for thermal-rigid-flexible coupling system

This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, varia- tional dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response be- tween the coupled system and the uncoupled system has re- vealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of con- sidering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate non- linear model and the linear model are clarified in detail.

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.

Design and Kinematics Analysis of Support Structure for Multi-Configuration Rigid-Flexible Coupled Modular Deployable Antenna

In order to meet the urgent need for diversified and multi-functional deployable antennas in many major national aerospace projects,such as interstellar exploration,the fourth phase of lunar exploration project,and the industrial application of Bei Dou,a deployable antenna structure composed of hexagonal prism and pentagonal prism modules is proposed.Firstly,the arrangement and combination rules of pentagonal prism and hexagonal prism modules on the plane were analyzed.Secondly,the spatial geometric model of the deployable antenna composed of pentagonal prism and hexagonal prism modules was established.The influence of module size on the antenna shape was then analyzed,and the kinematic model of the deployable antenna established by coordinate transformation.Finally,the above model was verified using MATLAB software.The simulation results showed that the proposed modular deployable antenna structure can realize accurate connection between modules,complete the expected deployment and folding functional requirements.It is hoped that this research can provide reference for the basic research and engineering application of deployable antennas in China.

MODEL OF CENTRIFUGAL EFFECT AND ATTITUDEMANEUVER STABILITY OF A COUPLEDRIGID-FLEXIBLE SYSTEM

The influences of nonlinear centrifugal force to large overall attitude motion of coupled rigid-flexible system was investigated. First the nonlinear model of the coupled rigid-flexible system was deduced from the idea of “centrifugal potential field', and then the dynamic effects of the nonlinear centrifugal force to system attitude motion were analyzed by approximate calculation; At last, the Lyapunov function based on energy norm was selected, in the condition that only the measured values of attitude and attitude speed are available, and it is proved that the PD feedback control law can ensure the attitude stability during large angle maneuver.

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.

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 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.

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.

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。

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。

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。

空间连杆引纬机构的刚柔耦合磨损分析

为准确预测空间连杆引纬机构间隙磨损机制,通过结合Lankarani-Nikravesh与Bai碰撞力模型,建立可变刚度与阻尼系数非连续接触碰撞力模型,采用改进的Coulomb摩擦力模型描述含间隙机构旋转铰的切向摩擦力,通过Lagrange方法对系统动力学建模;其次选取空间连杆为柔性化对象,综合Ansys与Adams分析,对空间连杆引纬机构进行刚柔耦合动力学仿真;最后将系统的动态仿真响应结果与Archard模型相结合,求解运动副磨损情况。结果表明:柔性构件可以有效缓解机构间隙碰撞的冲击作用,间隙为0.15 mm条件下,剑头加速度振荡最大幅值缩减53.2%;当间隙升至0.5 mm后,虽磨损范围大幅增加,但间隙磨损深度并未随之大幅提升。

基于刚柔耦合模型的多轴车辆平顺性仿真分析

针对采用一体化设计、整体式车身结构的多轴车辆,建立刚柔耦合虚拟样机模型,对多轴车辆的平顺性进行研究。基于驾驶室连接方式、驾驶室结构形式和驾驶室顶部连通形式3个设计要素,分析整车在不同载重和不同工况下的平顺性。分析表明,带有斜支撑桁架结构的驾驶室能够有效降低车辆行驶时驾驶室的加权加速度均方根值;顶部不连通的结构形式驾驶室舒适性更好;通过优化驾驶室结构形式和顶部连通形式,车辆在空载和满载情况下的平顺性得到了较大的改善,能够更好地满足使用要求。