Estimating the dynamic coefficient of friction from experimental data: the motion of a rocket inside a smoothbore launcher

The motion of a spinning rocket inside a smoothbore launcher has drawn some attention in recent years. The inaccuracy of spin-stabilized rockets can be attributed, in part, to the initial motion of the rocket inside the smoothbore launcher. Recently, tests have indicated that a closer examination of the problem is required. The tests were performed to determine the time history of the spin and forward motion of the rocket by Fastax cameras. The evaluation of the data with respect to engineering-design parameters is difficult since the experimental results must be compared with an analytical model of the system. In this paper, the results of one test are reported and a nonlinear analytical model is used which includes both the rotary and forward motion of the rocket. The two motions are coupled through a dynamic friction coefficient. The intent of this paper is to show how an analytical model can be made to fit the experimental data, that is, the initial conditions and the coefficient of friction are found which define the solution giving the best least-square fit to the data.     

旋转功能梯度智能结构的刚-柔耦合动力学分析

基于一次耦合模型理论建立了中心刚体-压电层-功能梯度材料智能梁系统的刚柔耦合动力学模型．研究了开环状态下将压电材料作为传感器的压电效应和质量刚度效应对系统动力学特性的影响．通过仿真算例与另两种不同建模理论（传统零次近似耦合模型、一次近似耦合模型）作了对比．随着中心刚体外驱动力矩的增大,零次近似耦合模型和一次近似耦合模型计算结果逐渐发散,而本文的一次耦合模型的计算结果始终保持收敛,较其他近似耦合模型具有一定优势．对三种不同的结构的计算结果表明,压电材料的压电效应对系统的动力学特性影响显著,压电材料的质量刚度效应也会影响智能梁的动力学行为,前者比后者的影响大得多．此外,功能梯度材料功能梯度指数对系统动力学特性的影响也较大．     

天线座驱动系统刚柔耦合动力学分析

为了分析天线座驱动系统的动力学特性,建立了一种新的多级齿轮传动系统动力学模 型------刚柔耦合模型,不仅考虑了轴的变形、轴承的支撑作用,而且采用了先进的轮齿接触模 型,克服了采用多体动力学方法研究齿轮系统动力学时存在的诸如忽略轴承的支撑作用、轴 的变形等缺陷. 动力学分析的计算结果和理论分析结果相一致,较准确地反映了该系统的齿 轮动力特性,对工程设计及性能校核具有指导意义.     

基于径向基点插值法的旋转Mindlin板高次刚柔耦合动力学模型

将无网格径向基点插值法(radial point interpolation method,RPIM)用于中心刚体?旋转柔性板的动力学分析.基于浮动坐标系方法和一阶剪切变形理论即Mindlin板理论,考虑剪切变形的影响,并计入板面内变形的非线性耦合变形项,采用径向基点插值法描述板的变形场,保留动能中有关非线性耦合变形项...     

MODEL OF CENTRIFUGAL EFFECT AND ATTITUDE MANEUVER STABILITY OF A COUPLED RIGID-FLEXIBLE SYSTEM

IntroductionThedynamicandcontrolofcoupledrigid_flexiblesystemisaleading_edgeresearchsubjectthathasdrawnextensiveattentionfromtheacademiccommunityintheworld[1].TheresearchconductedbyKaneetal.in 1 987[2 ]suggestedthat,thetraditionalmodelapplyingstructuraldynamicsassumptionaboutelasticdeformationindiscriminately[3,4 ],ineffect,hasneglectedtheso_called“dynamicstiffening”effectresultedfromcoupledrigid_flexiblesystem .Therefore ,itisofparticularimportancetoresearchtheactionofcoupledrigid_flexibles…     

考虑曲率纵向变形效应的大变形柔性梁刚柔耦合动力学建模与仿真

对在平面内做大范围转动的中心刚体柔性梁系统的动力学进行了研究,建立了考虑大变形效应的系统刚柔耦合动力学模型,并进行了动力学仿真.该动力学模型不但考虑了柔性梁横向弯曲变形和纵向变形(包含轴向拉伸变形和横向弯曲变形而引起的纵向缩短项),还考虑了纵向变形对曲率的影响,称为曲率纵向变形效应.在以往的研究中,柔性梁的横向弯曲变形能往往直接使用柔性梁横向弯曲变形来表达,并没有考虑纵向变形的影响.为了考虑柔性梁纵向变形对横向弯曲变形能的影响,在浮动坐标系下使用柔性梁参数方程形式的精确曲率公式来计算柔性梁的弯曲变形能.在此基础上建立了基于浮动坐标系的考虑曲率纵向变形效应的刚耦合动力学模型.论文给出了数值仿真算例,验证了本文所建的动力学模型既能适用于柔性梁的小变形问题,又能适用于大变形问题,且较现有高次刚柔耦合动力学模型更加适用于大变形问题的处理.论文还通过与能处理柔性梁大变形问题的绝对节点坐标法的比较,验证了模型的正确性.      

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.     

考虑剪切效应的旋转FGM楔形梁刚柔耦合动力学建模与仿真

本文对一类中心刚体-柔性梁系统在大范围转动下的刚柔耦合动力学问题进行了研究. 柔性梁为功能梯度材料(functionally graded materials, FGM)楔形变截面梁,材料体积分数在梁轴向呈幂律分布变化. 以弧长坐标来描述柔性FGM梁的几何位移关系,分别使用倾角和拉伸应变变量描述柔性梁的横向弯曲和纵向拉伸变形,并计及剪切效应. 采用假设模态法离散变形场,运用第二类拉格朗日方程进行方程推导,得到系统考虑剪切效应的刚柔耦合动力学模型. 基于全新的刚柔耦合动力学建模理论,研究不同轴向材料梯度分布的FGM楔形梁,通过数值仿真计算,分析讨论不同的转速、梯度分布规律以及变截面参数对系统动力学特性的影响. 结果表明,剪切效应对大高跨比的FGM楔形梁的变形影响较为明显,不容忽略;材料梯度分布规律和截面参数的选取均会对旋转FGM楔形梁的动力学响应和频率产生较大影响. 本文提出的考虑剪切效应的倾角刚柔耦合动力学模型是对以往非剪切模型的进一步完善,可应用于工程中的 Timoshenko梁结构的动力学问题求解.      

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.     

基于初应力法的作大范围运动柔性梁动力学建模理论研究

研究了初应力法的作大范围运动柔性梁的建模理论.根据连续介质理论,考虑应变-位移中的非线性项,用一致质量有限元法对柔性梁进行离散,基于Jourdain速度变分原理导出定轴转动下大范围运动为自由的柔性梁刚-柔耦合动力学方程.从其刚柔耦合动力学方程出发,考虑在大范围运动已知情况下的结构动力学方程.通过引入准静态概念,把其结构动力学方程转化为准静态方程.对纵向和横向变形节点坐标进行坐标分离,解出与纵向变形相关的准静态方程,得到准静态时的纵向应力表达式,从而获得附加刚度项.并对此非惯性系下作大范围运动柔性梁的结构动力学方程进行数值仿真,对零次近似模型、一次近似模型、初应力法动力学模型的仿真结果进行分析,揭示三种模型的动力学性质的差异.     

柔性梁刚柔耦合碰撞动力学及变形传播研究

运用柔性多体系统刚柔耦合动力学理论,研究了作大范围回转运动柔性梁的碰撞动力学问题.考虑柔性梁的横向变形,以及横向变形引起的纵向缩短项即非线性耦合变形项.采用基于Hertz接触理论及非线性阻尼理论的非线性弹簧阻尼模型来求解碰撞过程中产生的碰撞力,运用第二类拉格朗日方程建立了系统的刚柔耦合碰撞动力学方程.编制仿真软件进行动力学仿真计算,得到了碰撞力和系统动力学响应,对比分析了不同动力学模型对系统动力学响应的影响.同时研究了碰撞导致的柔性梁横向变形传播的波动特性.     

Dynamic analysis of a rotating rigid-flexible coupled smart structure with large deformations

Based on Hamilton's principle,a new kind of fully coupled nonlinear dynamic model for a rotating rigid-flexible smart structure with a tip mass is proposed.The geometrically nonlinear effects of the axial,transverse displacement and rotation angle are considered by means of the first-order approximation coupling(FOAC)model theory, in which large deformations and the centrifugal stiffening effects are considered.Three kinds of systems are established respectively,which are a structure without piezoelectric layer,with piezoelectric layer in open circuit and closed circuit.Several simulations based on simplified models are presented to show the differences in characteristics between structures with and without the tip mass,between smart beams in closed and open circuit, and between the centrifugal effects in high speed rotating state or not.The last simulation calculates the dynamic response of the structure subjected to external electrical loading.     

基于多体系统传递矩阵法的多管火箭定向器振动控制

应用多体系统传递矩阵法,建立了全新的多管火箭发射动力学控制模型,以二次型性能指标为成本函数, 设计了脉冲推力器为控制执行机构的振动主动控制律,并设计了多管火箭发射系统在燃气流冲击下定向器的振动主动控制系统,获得了最优脉冲控制力幅值和脉冲推力器工作次数. 应用设计的控制律数值仿真了某多管火箭定向器无控和受控状态下的振动响应,仿真结果表明该法可有效地降低定向器的振动.该方法易于工程实现,对控制多管火箭发射系统的振动、提高多管火箭射击的精度具有重要意义.      

Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.     

湿式发射对同心筒瞬态热冲击的影响机理

针对路基同心筒自力发射整体热环境恶劣的问题,依托弹性变形和域动分层相结合的动网格技术,基于均质多相流理论并耦合液态水专用汽化求解程序,建立在发射筒底部注水的三维气液两相流体动力学模型;以火箭发动机自由射流注水实验为基础,验证汽化程序三维计算的可靠性与有效性;通过瞬态数值计算,讨论筒底注水角度对导弹、内外筒热环境和导弹载荷特性的影响规律。分析表明:发射筒内发生了显著的汽化反应;导弹及发射系统总体热环境得到了显著改善,实现了发射系统持续降温的目的;在筒底注水后,弹底的附加推力及火箭发动机的推力有一定增加,随着注水量的减少,注水对导弹载荷的影响越来越弱。     

一类分段光滑非线性平面运动系统响应特性研究

针对由一个线性子系统和一个非线性子系统构成的两自由度非自治分段光滑非线性平面运动系统的响应特性开展了研究. 该分段光滑非线性模型可用来确定对称转子/定子系统的主要碰摩响应, 且在反映非光滑系统典型特性上具有明显的特征:(1) 切换分界面是由两自由度坐标共同决定的一个幅值曲面;(2) 子系统周期解与分界面的擦碰, 不是发生在一个点上, 而是同时发生在解的所有点上;(3) 完整系统未发现由两子系统共同作用而产生的周期解. 因此, 对于该非光滑系统响应特性的研究, 很难直接利用目前有关非光滑系统平衡点和周期解分岔分析的方法. 为此, 尝试了根据子系统的响应特性, 划分出完整系统响应对分界面处切换的敏感区和非敏感区, 并针对非敏感区可由子系统解的特性求得完整系统的响应, 而针对敏感区通过子系统动力学特征的分析有助于解释完整系统响应的生成机制.     

作大范围空间运动柔性梁的刚-柔耦合动力学

研究带中心刚体的作大范围空间运动梁的刚-柔耦合动力学问题．从精确的应变-位移关系式出发,在动力学变分方程中,考虑了横截面转动的惯性力偶和与扭转变形有关的弹性力的虚功率,用速度变分原理建立了考虑几何非线性的空间梁的刚-柔耦合动力学方程,用有限元法进行离散．通过对空间梁系统的数值仿真研究扭转变形和截面转动惯量对系统动力学性态的影响．     

刚柔耦合定位平台结构-运动-控制一体化建模

针对微电子制造行业等领域中的长行程高精度定位问题,提出了一种刚柔耦合定位平台,并建立了其结构-运动-控制一体化动力学仿真模型。首先,根据刚柔耦合定位平台的结构特点对浮动坐标法进行修改,建立了简洁高效的动力学仿真模型。其次,结合动力学模型、3阶S型曲线和经典的PID控制方法建立了结构-运动-控制一体化仿真模型。最后,通过数值算例对仿真模型的有效性进行了验证。数值模拟结果显示,建立的结构-运动-控制一体化仿真模型能够有效地对定位平台的工作过程进行模拟,为后续的结构优化、运动规划和控制系统设计等工作创造条件。     

A multi-sensing scheme based on nonlinear coupled micromachined resonators

A new multi-sensing scheme via nonlinear weakly coupled resonators is introduced in this paper, which can simultaneously detect two different physical stimuli by monitoring the dynamic response around the first two lowest modes. The system consists of a mechanically coupled bridge resonator and cantilever resonator. The eigenvalue problem is solved to identify the right geometry for the resonators to optimize their resonance frequencies based on mode localization in order to provide outstanding sensitivity. A nonlinear equivalent model is developed using the Euler–Bernoulli beam theory while accounting for the geometric and electrostatic nonlinearities. The sensor's dynamics are explored using a reduced-order model based on two-mode Galerkin discretization, which reveals the richness of the response. To demonstrate the proposed sensing scheme, the dynamic response of the weakly coupled resonator is investigated by tuning the stiffness and mass of the bridge and cantilever resonators, respectively. With its simple and scalable design, the proposed system shows great potential for intelligent multi-sensing detection in many applications.