A rigid-flexible coupling finite element model of coupler for analyzing train instability behavior during collision

Rail vehicles generate huge longitudinal impact loads in collisions.If unreasonable matching exists between the compressive strength of the intermediate coupler and the structural strength of the car body,the risk of car body structure damage and train derailment will increase.Herein,a four-stage rigid-flexible coupling finite element model of the coupler is established considering the coupler buckling load.The influence of the coupler buckling load on the train longitudinal-vertical-hori-zontal buckling behavior was studied,and the mechanism of the train horizontal buckling instability in train collisions was revealed.Analysis results show that an intermediate coupler should be designed to ensure that the actual buckling load is less than the compressive load when the car body structure begins to deform plastically.The actual buckling load of the coupler and the asymmetry of the structural strength of the car body in the lateral direction are two important influencing factors for the lateral buckling of a train collision.If the strength of the two sides of the car body structure in the lateral direction is asymmetrical,the deformation on the weaker side will be larger,and the end of the car body will begin to deflect under the action of the coupler force,which in turn causes the train to undergo sawtooth buckling.

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]

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.

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.

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.

An analysis on a rigid-flexible coupling system of an oscillating massand a rotating disk

A mass-rod-disk system consisting of an oscillating mass attached to a rigid rotating disk by an elastic rod is designed to study rigid-flexible coupling mechanism.Suppose the rod is lightweight and has enough stiffness,the theorems of linear momentum and angular momentum are applied to the mass-rod-disk system based on the kinematic description of the system.With respect to two deflections of the mass and one angular velocity of the system,a group of nonlinear differential equations are established where the tangential inertial force,centrifugal force,Coriolis force as well as the moments of additional inertial forces take important effects on the dynamic response.For the sake of description,these three types of inertial forces mentioned before are referred to as additional inertial forces in this paper.The horizontal deflections of the mass and the angular velocity of the disk rotating about a fixed-axis are numerically solved for the prescribed external torque.The oscillating trajectory of the mass is deeply influenced by the additional inertial forces,meanwhile the dynamic fluctuations of the angular velocity and rotary inertia of the system are strongly affected by the mass oscillation.

INVESTIGATION OF ACTIVE CONTROL FOR DYNAMIC STABILITY OF HELICOPTER ROTOR－BODY COUPLING

A study is conducted on the feasibility of helicopter ground and air resonanceby using actively controlled tabs mounted at the trailing edge of an aerofoil. A method isdeveloped to obtain the optimal feedback control law through constructing a referencemodel according to requirements of stability levels in the modal space. The effects of rotorspeed and length and location of tabs on the control law are analyzed, and it is found possible that a controller can be designed into constant feedback gain against rotor speed andto feed back only to the dominant system states to eliminate the unstable range of rotorspeed.

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.

Numerical simulation of aircraft arresting process with an efficient full-scale rigid-flexible coupling dynamic model

The arresting process of carrier-based aircraft is widely recognized as a challenging task,characterized by the highest accident rate among all carrier-based aircraft operations.Dynamic simulation plays a crucial role in assessing the intricate responses of the arresting process,favoring the design of carrier-based aircraft.An efficient and accurate rigid-flexible coupling model for analyzing the dynamic response of the arresting process is proposed.By combining the dynamic characteristics of airframe,landing gear,arresting hook and arresting gear system,the rigid-flexible coupling dynamic model is established to reflect the relative motion of the coupling parts and arresting load.The dynamic model is verified through simulations of landing gear landing drops and by comparing the arresting simulation results with corresponding data in the US military standard.Additionally,simulations of the arresting process under different off-center distance and aircraft yaw angle are conducted to obtain the dynamic response of the aircraft during the arresting process.The result indicates that the rigid-flexible coupling dynamic model proposed is effective for analyzing the arresting dynamics response of carrier-based aircraft.The axial force of the arresting cable on both sides of the hook engagement point,pitch and yaw angle of aircraft are inconsistent under yaw and off-center arresting.The analysis method and obtained results provide valuable references for assessing the dynamic responses of carrier-based aircraft during arresting process and offer valuable in-sights in the design of carrier-based aircraft.

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.

Monolithic Coupling of the Pressure and Rigid Body Motion Equations in Computational Marine Hydrodynamics

In Fluid Structure Interaction(FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned manner by solving the rigid body motion equations once per nonlinear correction loop, updating the position of the body and solving the fluid flow equations in the new configuration. The partitioned approach requires a large number of nonlinear iteration loops per time–step. In order to enhance the coupling, a monolithic approach is proposed in Finite Volume(FV) framework,where the pressure equation and the rigid body motion equations are solved in a single linear system. The coupling is resolved by solving the rigid body motion equations once per linear solver iteration of the pressure equation, where updated pressure field is used to calculate new forces acting on the body, and by introducing the updated rigid body boundary velocity in to the pressure equation. In this paper the monolithic coupling is validated on a simple 2D heave decay case. Additionally, the method is compared to the traditional partitioned approach(i.e. "strongly coupled" approach) in terms of computational efficiency and accuracy. The comparison is performed on a seakeeping case in regular head waves, and it shows that the monolithic approach achieves similar accuracy with fewer nonlinear correctors per time–step. Hence, significant savings in computational time can be achieved while retaining the same level of accuracy.

Optimal control of attitude for coupled-rigid-body spacecraft via Chebyshev-Gauss pseudospectral method

The attitude optimal control problem （OCP） of a two-rigid-body space- craft with two rigid bodies coupled by a ball-in-socket joint is considered. Based on conservation of angular momentum of the system without the external torque, a dynamic equation of three-dimensional attitude motion of the system is formulated. The attitude motion planning problem of the coupled-rigid-body spacecraft can be converted to a dis- crete nonlinear programming （NLP） problem using the Chebyshev-Gauss pseudospectral method （CGPM）. Solutions of the NLP problem can be obtained using the sequential quadratic programming （SQP） algorithm. Since the collocation points of the CGPM are Chebyshev-Gauss （CG） points, the integration of cost function can be approximated by the Clenshaw-Curtis quadrature, and the corresponding quadrature weights can be calculated efficiently using the fast Fourier transform （FFT）. To improve computational efficiency and numerical stability, the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of state and con- trol variables. Furthermore, numerical float errors of the state differential matrix and barycentric weights can be alleviated using trigonometric identity especially when the number of CG points is large. A simple yet efficient method is used to avoid sensitivity to the initial values for the SQP algorithm using a layered optimization strategy from a feasible solution to an optimal solution. Effectiveness of the proposed algorithm is perfect for attitude motion planning of a two-rigid-body spacecraft coupled by a ball-in-socket joint through numerical simulation.

On the Stability Analysis of a Coupled Rigid Body

In this research article, we investigate the stability of a complex dynamical system involving coupled rigid bodies consisting of three equal masses joined by three rigid rods of equal lengths, hinged at each of their bases. The system is free to oscillate in the vertical plane. We obtained the equation of motion using the generalized coordinates and the Euler-Lagrange equations. We then proceeded to study the stability of the dynamical systems using the Jacobian linearization method and subsequently confirmed our result by phase portrait analysis. Finally, we performed MathCAD simulation of the resulting ordinary differential equations, describing the dynamics of the system and obtained the graphical profiles for each generalized coordinates representing the angles measured with respect to the vertical axis. It is discovered that the coupled rigid pendulum gives rise to irregular oscillations with ever increasing amplitude. Furthermore, the resulting phase portrait analysis depicted spiral sources for each of the oscillating masses showing that the system under investigation is unstable.

The Development of Hi-Speed Punching System Using A Couple of Rotating Bodies

Punched steel sheets (metal sheets or foils) as thi n as 0.1mm are quite useful in the field of filters and various precision instrume nts. Thus, we have to develop more accurate and speedy techniques for punching t hin sheets. The traditional punching method uses an up-down pressing motion of a punch or a die on a strip of metal. The efficiency of this method is determine d by the speed of the motion. In the case of punching a sequence of tiny holes w ith a few millimeters’ interval, the speed of feeding a strip of metal to the p unching machine cannot exceed only a couple of meters per minute. We have de veloped a new technique for punching tiny holes with a pair of rotating bodies i n order to increase the feeding speed up to 100 meters per minute. Our proposed technique is shown in Fig.1 where the female tool has a round blade and the male tool has an M-shape boss. In addition, the setting of two tools i s alternating. The interference between them cannot occur because the clearance between the front and the back edge of the male tool and the female tool in the rotating direction becomes infinite in this configuration. An appropriate cleara nce is given for the thickness of the sheet between the side edge of the male to ol and the female tool. The punching itself is done by shearing. The side edge o f the male tool does contact with the female tool, but they cannot be interferin g. Our technique has another advantage to the traditional up-down pressing mach ine where the stamped out chips are hard to be discharged. It is quite easy in o ur proposed technique. Fig.2, 3 show a sample of punched material [TPP116A,+39mm88mm,Y,PZ#]Fig.1 The configuration of the punching parts using the sequential punching system.[TPP116B,+43mm155mm,X,BP#]Fig.2 A sample of punched material using the continuous punch ing lineFig.3 A exterior picture of a piece of punched steel foil(coi l) using the continuous punching For our developed high speed punching system, it is shown for (1) the configurat ion of punching tool and the punching mechanism, (2) the influence of male shape on punched hole quality, (3) the outline of continuous punching system, (4) the relation between punching speed and accuracy of hole pitch and hole dimensi on, (5) the mechanical property of punched metal sheet and (6) capability of hig her punching.

海上浮式风机多体系统耦合动力模型研究

海上浮式风机是近年来随着海上风电的快速发展,为了捕获深海更丰富、更持久的风能而提出的一种风力发电装置,已成为当今风能开发的主要方向。作为一种多体系统,由于海上浮式风机结构特殊,加上环境复杂,对其进行准确的计算和分析尤为重要。本文对海上浮式风机的耦合动力模型进行了研究,建立了复杂工况下Spar型海上浮式风机改进的14-DOF耦合动力模型,包括气动力模块、水动力模块和结构分析模块等,用于扩展其适用范围和准确计算风机的动力响应,并通过数值仿真对所建模型进行了分析和验证。主要的改进有:不对平台和塔架的转动角度作小量近似,扩展其适用范围;考虑角速度和欧拉角速度的换算关系,不作等化处理。此外,所建模型考虑风机叶片扭转角对叶片变形的影响,得到了较为准确的叶片面内外响应。同时采用线性势流理论对水动力进行计算,较之Morison方程适用性更广。仿真分析表明,本文所建模型可以更准确地计算海上浮式风机系统的动力响应,且具有更广的适用范围。

风浪联合作用下分布式调谐质量阻尼器对海上半潜漂浮式风机的减振控制

海上半潜漂浮式风机在复杂深海环境下产生有害振动会威胁风机的安全性和耐久性,针对该问题并结合美国NREL的5 MW样机的漂浮平台几何结构构造,提出利用分布式调谐质量阻尼器(Tuned Mass Dampers,TMDs),即分别在漂浮平台的3根浮筒中布置TMD,形成等边三角形布置,对随机风浪联合作用下海上半潜漂浮式风机的平台纵摇振动进行控制。为了更好地描述分布式TMDs对海上半潜漂浮式风机的减振效果,基于拉格朗日方程和模态叠加法,对海上半潜漂浮式风机-TMDs耦合系统提出并建立了9自由度多体动力学模型。基于H_(∞)算法,即以平台纵摇频响函数的峰值为优化目标,对分布式TMDs的参数进行优化设计,优化设计中考虑了3个TMDs之间的耦合关系。对风机-TMDs耦合系统开展了风浪联合作用下的数值模拟,分析了分布式TMDs对平台纵摇响应的减振效果。结果表明:最优设计下的分布式TMDs对海上半潜漂浮式风机平台纵摇振动具有良好的减振性能;在三种不同工况的随机风浪荷载作用下,分布式TMDs对平台纵摇固有频率附近的功率谱密度曲线峰值减振率和标准差减振率能分别达到39%和52%以上。

捣固装置与有砟道床相互作用及捣固频率的影响研究

捣固频率是大型养路机械作业的关键参数,影响捣固作业动力作用及养修效果。基于压电效应研发了能适应复杂、恶劣捣固作业环境的动态冲击力传感器,自主设计了高精度、高时效的捣镐冲击力测试方法,通过现场试验研究了捣固频率对捣镐冲击力及道床力学质量状态的影响;基于离散元与多柔性体动力学耦合算法构建了捣固装置-有砟轨道精细化系统模型,通过仿真计算研究了捣固频率对道砟受力特征及运动行为的影响。结果表明:在一定范围内增大捣固频率可减小捣镐冲击力,同时提高道床力学质量状态;当捣固频率为30 Hz~40 Hz时,道砟受力相对较小,最不易发生劣化现象,且道砟运动最充分,养修效果最佳。

基于双向耦合法的采煤机螺旋滚筒振动特性分析

为研究采煤机螺旋滚筒在多种赋存条件下的振动特性,以MG2×55/250–BWD型薄煤层采煤机为工程对象,优化煤岩接触模型,建立与实际赋存条件相似的多种不同截割工况下煤壁离散元模型。结合DEM–MFBD(Discrete Element Method-Multi Flexible Body Dynamics)双向耦合数值模拟方法搭建采煤机截割部刚柔耦合虚拟样机模型与煤壁离散元模型的双向耦合试验平台,通过仿真试验得到不同煤岩工况下螺旋滚筒的截割过程,并分别对其振动特性的变化规律展开分析。研究结果表明:螺旋滚筒在截割过程中,三向均出现不同程度的振动,其中截割阻力方向振动加速度最大,牵引阻力方向振动加速度次之,侧向力方向振动加速度最小。随着模型中夹矸硬度以及层数比例的增加,截割过程中螺旋滚筒的振动强度不断加剧,最大振动加速度有效值的差值达到4403.149 mm/s^(2)。利用短时傅里叶变换将一维振动信号转化为二维时频谱图像,得到不同煤岩工况下振动信息变化特征在时频域中完成较好保留,其时频谱图像的特征样本效果优于各工况的时域一维信号曲线,主频能量位置、范围大小、特征团形状等信息具有明显区别,即使遇到夹矸层数不同,夹矸坚固性系数也存在差异的复杂工况,其时频谱图像中能量特征的分布形式也具有显著差别。通过振动模态分析发现,随着煤壁中含有夹矸硬度的增加,各部位的变形量均发生变化,其中截齿部位变化最为强烈。基于相似理论搭建采煤机振动信号测试试验平台,对不同煤岩工况条件下螺旋滚筒截割过程进行了测试研究,通过追踪螺旋滚筒的振动状态,发现其振动变化规律与双向耦合数值模拟一致。试验测试得到DEM–MFBD数值模拟方法获取的螺旋滚筒振动加速度有效值与依据相似比反推的试验数据之间的误差小于DEM离散元数值模拟方法与实验数据之间的误差,验证了DEM–MFBD数值模拟方法的准确性。研究结果对于提升螺旋滚筒工作可靠性具有重要意义,同时也为采煤机智能化开采的煤岩截割状态识别系统搭建过程中数据信息的获取提供了一种新的方法。

极端风浪下海上机场VLFS连接器载荷响应分析

为了研究浪向角、入射波频率和连接器刚度耦合变化对连接器载荷的影响,以刚模块柔性连接器(rigid module and flexible connector,简称RMFC)模型计算理论为基础,建立8模块海上机场超大浮体水动力模型进行数值模拟水槽实验,分别对连接器在规则波和不规则波下的载荷响应进行频域计算。选取6个连接器刚度条件,研究不同连接器刚度下连接器的载荷响应,在不同海况和连接器刚度条件下考虑0°,30°,45°,60°及90°浪向角的作用,连接器载荷响应幅值主要从纵向、横向及垂向3个方向进行比对。结果表明,同一方向上的载荷在浪向角45°和60°较为敏感,极端风浪耦合环境下,垂向载荷明显比其他两个方向载荷值大,连接器载荷值随刚度值增大而增大,在K5~K6之间呈大幅递增趋势。