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 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.

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.

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.

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.

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.

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。

基于修正Manson-Halford模型的破碎机销轴疲劳分析

以双级锤式破碎机为研究对象,考虑销轴所受载荷的加载次序和载荷之间相互作用对销轴疲劳损伤的影响,对Manson-Halford(M-H)非线性疲劳损伤模型进行了修正,并通过试验数据验证了修正后模型的准确性和可靠性;考虑到破碎过程中锤头与销轴之间存在的非线性碰撞接触和物料颗粒对销轴受力的影响,利用MFBD-DEM双向耦合的方法获取了销轴的动态载荷;最后基于修正后M-H模型对销轴进行了疲劳分析。结果表明,与现有模型相比修正后的M-H模型寿命预测的误差最小;基于修正后M-H模型计算得到销轴的最小疲劳寿命为9.918×10^(6)次(165 h);利用MFBD-DEM双向耦合方法对双级锤式破碎机等大型破碎设备进行疲劳分析是合理可行的。

TYZN-06-04机器人刚柔耦合工况下的运行过程探究

以TYZN-06-04六自由度关节机器人为研究对象,使用ADAMS构建机器人刚柔耦合仿真模型,将生成的运行轨迹导入ADAMS中,通过刚柔耦合仿真模型分别探究机器人运行速度、运行加速度和负载对其定位精度误差的影响,以便研究在不同运行速度、运行加速度及不同负载的情况下,机器人执行末端的位置误差变化情况,最终实现Matlab的曲线数据拟合,直观呈现机器人刚柔耦合工况下运行过程的变化规律,根据运行过程变化规律,采取相应的位置精度误差分析及误差补偿措施。

中心刚体-形状记忆合金层合功能梯度梁的动力学特性研究

文章对中心刚体-形状记忆合金层合功能梯度梁系统在平面内作大范围运动进行动力学特性研究。SMA层采用多项式的形状记忆合金的本构模型和假设的层合部分的功能梯度分布,在考虑横向变形引起纵向变形的非线性耦合量。采用假设模态法对SMA层合FGM梁系统进行离散,运用第二类Lagrange方程推导得到系统高次刚柔耦合模型,编写软件程序进行动力学仿真。研究了形状记忆合金层的在不同功能梯度下温度对动力学特性的影响以及不同温度下增加SMA层厚度对动力学特性的影响。研究结果表明温度和SMA层厚度对系统的动力学特性影响较大。

路基不均匀沉降对高速车辆-道岔系统动力特性的影响

为了研究路基不均匀沉降对高速列车过岔时轮轨动力响应的影响,结合多体动力学和有限元法,考虑道岔多钢轨的相互作用及柔性变形,建立高速列车-道岔刚柔耦合动力学模型,分析路基不均匀沉降位置、沉降波长、沉降幅值、行车速度等因素对高速列车过岔安全性和平稳性的影响。结果表明:高速道岔区发生路基不均匀沉降会导致轮轨力和车体加速度增加,降低车辆过岔的安全性和平稳性,当路基不均匀沉降最大值位于尖轨顶宽15 mm断面时,对车辆过岔的动力学行为影响最大,轮载过渡段的长度较无路基不均匀沉降条件下延长25.64%;各项动力学指标随路基不均匀沉降波长增大而减小,随沉降幅值增大而增大;相比于区间线路,当道岔区发生路基不均匀沉降时,行车速度的变化对动力学响应的影响更大,尤其是轮轨横向力和车体横向振动加速度。

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.

薄壁四点接触球轴承-腕部关节系统接触动力学分析

在机器人实际工况中,针对含有薄壁四点接触球轴承的机器人腕部关节系统的运动稳定性问题,对腕部系统模型进行了简化设计和仿真研究。在考虑薄壁结构的弹性变形和动态接触作用耦合影响的基础上,建立了刚柔耦合工业机器人腕部关节系统模型,分析了不同受载工况和正反转驱动下的变形规律和动态特性。首先,基于多体动力学和Hertz接触理论,设计了包含薄壁四点接触球轴承和中空轴及基座的腕部关节系统刚柔耦合接触动力学仿真模型;然后,考虑薄壁中空轴、基座、轴承套圈和保持架的结构弹性变形、钢球和套圈滚道、保持架的动态接触作用,研究了机器人腕部关节系统两种实际工况对保持架和钢球角速度、保持架和薄壁基座振动位移、钢球与套圈的动态接触力的影响;最后,计算分析了两种工况下腕部关节系统的动态载荷规律和振动响应特性。研究结果表明:在相对较大的径向载荷作用下,保持架和钢球会出现打滑现象,速度呈现周期波动,保持架和基座具有更好的运动稳定性,其薄壁轴承内部载荷降低,主副接触对均承担联合载荷,轴承内部载荷稳定性也更好。该仿真模型及结果可以为薄壁腕部关节系统的动力学分析与设计提供参考。