含间隙铰的机械多体系统动力学模型

对四类间隙铰模型(连续接触模型、有限元模型、经典碰撞模型和接触变形模型)进行分析比较，给出了经典碰撞和接触变形模式的含间隙多体系统动力学模型。经典碰撞模式的动力学模型着重考察系统动力学的整体行为，不能预测碰撞过程中铰关节局部接触力的变化历程。接触变形模式的多体系统动力学模型考虑了碰撞体间的法向和切向接触力，以及阻力矩，能够求解系统运动过程中间隙铰轴销与孔体的碰撞力。采用间隙铰的非线性弹簧阻尼模型，研究了重力场及其方向性对空间可展机构动力学性能的影响。计算结果表明，无重力与有重力环境时含间隙可展机构动力学行为有较大地差别，重力作用使间隙铰内碰撞减弱。为了保证在地面试验中可靠地预测在太空展开性能，可展机构在地面试验时应采取重力补偿措施。     

柔性多体系统含摩擦碰撞stick-slip过程动力学仿真

基于高次刚柔耦合理论和Lagrange乘子法,研究了柔性多体含摩擦碰撞stick-slip过程的全局动力学的精确建模与自动切换仿真问题。基于变拓扑思想,根据分离、碰撞、黏滞接触和滑动接触等状态分别构造相应的约束条件和动力学方程。运用冲量/动量法求解碰撞初始条件;引入切向滑动摩擦力势能的概念描述切向滑动接触力;给出接触、分离、黏滞、正向/逆向滑动状态之间的切换准则,实现了系统全局动力学自动切换。通过算例的数值仿真,分析了滑移/黏滞(微滑动)、正/逆向滑动等复杂非光滑现象,验证了该模型和算法的有效性。     

含摩擦碰撞柔性机械臂动力学研究

本文研究了由柔性杆、柔性铰构成的机械臂的斜碰撞动力学问题。首先,采用高次刚柔耦合理论通过Lagrange方程得到系统的递推动力学模型。然后,引入碰撞力势能,运用连续法建模获得碰撞力所对应的广义力,得到系统的碰撞动力学方程。采用Hertz接触模型和Coulomb摩擦光滑修正模型分别建立法向和切向碰撞模型,提出碰撞/分离切换准则。通过光滑化处理摩擦接触,提高了大型复杂柔性多体系统含摩擦碰撞全局动力学的计算效率。最后对国际空间站机械臂Canadarm2的简化模型斜碰撞过程进行仿真,验证了所提模型和算法的有效性。     

火箭橇靴轨接触特性数值分析

为研究火箭橇靴轨接触特性,采用Eluer-Bernouli梁单元对火箭橇橇体进行离散,建立了考虑轨道不平顺度的靴轨非线性接触力模型,通过Newmark-β结合Newton-Raphson局部迭代求解包含靴轨非线性接触力的橇轨动力学方程,并通过试验验证了数值解的正确性,数值计算结果表明:在700 m/s速度下,靴轨接触力...     

多体非连续变形系统的计算力学模型及其应用

针对由不同特性物体所组成的多体系统,探讨了能够涵盖各种变形状态和运动形式的广义有限单元模式及其插值函数形式。对于多体接触问题,发展了能够合理描述界面特性的接触力元模型,即采用某种应力插值函数将界面上的相互作用力由接触对上的接触应力来表达,并将接触对上的接触应力当作需满足界面上屈服准则与流动法则等状态控制条件的参变量,将其作为约束条件加入系统控制方程。根据非连续变形系统的分区参变量最小势能变分原理,联立变分驻值条件与参变量的状态控制条件建立了多体系统非连续变形计算力学分析的基本控制方程,将问题最终归结为一个含有自由变量和等式约束条件的线性互补问题,对此发展了数值解法,并进行了多个算例的数值分析。计算结果表明该模型不仅能够对多体系统进行静、动力耦合分析,而且还能够模拟多体系统的变形与应力及接触界面上的接触应力和相对运动等复杂的非线性过程。     

冗余约束多刚体系统摩擦碰撞问题的数值求解方法

针对冗余约束多刚体系统的摩擦碰撞问题,以牛顿恢复系数作为碰撞终止条件,以离散化的系统动力学方程和线性规划理论为基础,建立了相应的混合互补模型。为有效求解该模型,利用最小二乘法和线性化方法,将混合互补模型转化为标准的线性互补模型,用线性互补模型的求解算法进行数值求解。接着,提出一种直接投影修正算法对碰撞计算过程进行修正,有效防止了碰撞加剧约束违约的现象。最后,通过一个算例,验证了数值求解方法和修正算法的有效性。     

摩擦接触裂纹问题的扩展有限元法

扩展有限元法(XFEM)是一种在常规有限元框架内求解强和弱不连续问题的新型数值方法。扩展有限元法分析闭合型裂纹时,必须考虑裂纹面间的接触问题。已有文献均采用迭代法求解裂纹面的接触问题。该文建立了闭合型摩擦裂纹问题的扩展有限元线性互补模型,将裂纹面非线性摩擦接触转化为一个线性互补问题求解,不需要迭代求解。算例分析说明了该方法的正确性和有效性,同时表明扩展有限元法结合线性互补法求解接触问题具有较好的前景。     

柔性多体系统碰撞动力学研究

摘 要：针对工程中常见的柔性多体系统碰撞过程,详细的分析了柔性多体系统的接触碰撞条件,基于非线性等效弹簧阻尼模型建立了柔性体的碰撞模型,并基于库仑摩擦模型考虑两体碰撞时的切向摩擦作用。在此基础上把柔性体碰撞模型综合到柔性多体系统动力学方程中,建立了含接触碰撞的柔性多体系统动力学模型,此模型适用于一般含碰撞的多体系统。仿真算例以柔性梁在重力场中的接触碰撞过程为对象进行动力学仿真,研究柔性梁碰撞前、碰撞过程及碰撞后的动力学特性和动态响应,以及碰撞过程碰撞力的变化规律,并与刚性梁在重力场中的接触碰撞过程进行详细的比较和分析,结果表明基于非线性等效弹簧阻尼模型建立的柔性多体系统碰撞动力学模型可以有效的分析接触碰撞过程的动力学性能,验证了模型的有效性和正确性。     

多柔性体系统动力学的有限元方法(MUFEM)

本文探讨多柔性体系统动力学的一种新的数值仿真方法一多体有限元方法（MultibodyFiniteElementMethod,MUFEM）。MUFEM以有限元方法为基础,综合区域分解法（DDM）和非连续体变形分析方法（DDA）的主要优点。MUFEM的主要特点是：1）构造边界网格描述系统动态变化的拓扑几何关系;2）采用FEM模型和类似子结构的方法分析多柔性体系统的动力学特性;3）各子块之间可能接触边界的非连续性用Lagrange乘子处理;4）摩擦接触问题用非线性数学规划方法求解。算例表明,MUFEM能很好模拟多柔性体系统的运动以及相互之间的作用,有良好的发展前景。     

考虑三维圆柱铰间隙碰撞的空间机构柔性多体动力学分析方法

三维圆柱铰的动态性能对空间机构的运动精度和动力学特性有着重要的影响。基于多体动力学方法和刚体有限元方法,提出考虑三维圆柱铰的间隙碰撞和动态接触作用的空间机构柔性多体接触动力学方法。采用圆柱-圆柱的线接触力学模型和切片法,计算圆柱-圆柱的接触变形量和接触力,建立三维圆柱铰的轴销与轴套之间的间隙碰撞作用和三维动态接触关系。以等效刚体单元和Timoshenko梁单元描述柔性杆件的刚性有限元模型,建立柔性连杆和三维圆柱铰的具有多刚体系统的统一形式的动力学方程。计算分析了含三维圆柱铰的空间机构的运动精度和动力学特性,获得空间机构的位移响应,三维圆柱铰的相对运动轨迹和动态作用力等动力学响应。采用三维圆柱-圆柱动态线接触方法,能有效地预测空间机构系统的三维圆柱铰持续接触、间隙碰撞状态和摩擦作用下的动力学特性。计算结果表明三维圆柱铰的间隙碰撞作用对空间机构的运动精度和动态特性的影响较为显著。动力学模型和计算结果对复杂工况下高精度多间隙的空间机构的动态设计和动力学研究具有重要的理论意义。     

A new non-smooth model for three dimensional frictional contact problems

This paper presents a new non-smooth model for three dimensional contact problems with Coulomb friction. The problem is formulated exactly as a system of non-smooth equations without employing any external variables or approximation. As compared with the existing models, the present model does not utilize the slip angle as a variable. Therefore, transformation of variables is not required and the formulation is simpler. For solving a three dimensional contact problem, the nodus is to determine the slip direction at the contact nodes because the relative slipping of the contact may occur in any direction on the contact interface. The proposed model solves this problem in a simple manner by formulating it as an equivalent non-smooth equation. Based on the theory of non-smooth analysis, a generalized derivative is introduced to solve the non-smooth equations. Thus, the non-smooth damped Newton method can be implemented directly. The proposed method has been tested using a number of numerical examples. Received 23 March 2000     

A Differential Quadrature as a numerical method to solve differential equations

A Differential Quadrature proposed here can be used to solve boundary-value and initial-value differential equations with a linear or nonlinear nature. Unlike the classic Differential Quadrature Method (DQM), the newly proposed Differential Quadrature chooses the function values and some derivatives wherever necessary as independent variables. Therefore, the δ-type grid arrangement used in the classic DQM is exempt while applying the boundary conditions exactly. Most importantly, the explicit weighting coefficients can be obtained using the proposed procedures. The present method is used to solve two types of differential equations which are the single-span Bernoulli–Euler beam's buckling equation and the one-degree-of-freedom solid dynamic equation. Excellent results were obtained. Received: 4 January 1999     

含摩擦柱铰链平面多体系统动力学的建模和数值方法

以含摩擦柱铰链平面多体系统为研究对象,建立其动力学方程并给出相应的数值计算方法。首先,建立了含摩擦转动柱铰链的力学模型。在此基础上,应用第一类Lagrange 方程给出了该类系统的动力学方程,将Lagrange乘子与柱铰链的法向约束力建立了对应关系,并给出了柱铰链摩擦力的广义力。由于摩擦力的存在,使得该方程是关于Lagrange 乘子的分段连续的非线性代数方程组,该文对此采用混合算法:对于连续段(物体相对转动的角速度不为零时),采用拟牛顿算法和龙格-库塔法求解方程;在不连续点(物体相对转动的角速度为零时),通过粒子群算法(PSO)、试算法和龙格-库塔法求解方程,克服了方程在不连续处Lagrange 乘子(法向约束力)的初值不易选取的困难。最后,通过算例说明了该算法的有效性和可行性。     

Unified nonlinear quasistatic and dynamic analysis of RF-MEMS switches

In this paper, the modified couple stress-based strain gradient theory is used to provide a unified nonlinear model of the quasistatic and dynamic behavior of an electrostatic microelectromechanical systems microbeam capacitive switch of the Euler–Bernoulli type. Our model not only accounts for the contact between the microbeam and the dielectric substrate using nonlinear springs and dampers, but also accounts for the system size by introducing an internal material length scale parameter. In view of the size of the microbeam and electrostatic gaps involved, Casimir and Van der Waals forces, damping force due to the squeeze membrane effect and electrostatic force with first-order fringing field effects were accounted for in our model. The resulting nonlinear system of PDEs was expanded into a coupled system using series expansion and integrated into ODEs using weighted residuals of the Galerkin type. To overcome the difficulties associated with the determination of the contact length, the Heaviside function for deflection was replaced with a Heaviside function for the contact length, and an iterative procedure was adopted to determine the contact length. To obtain the time variation of the microbeam, the dynamic system of equations was solved using Newmark’s integration scheme. The outcome of our work shows the dependence of the pull-in voltage upon the inertia force, slenderness ratios of the microbeam, the electrostatic gap and the initial boundary conditions of the switch. In addition, we were also able to provide the full history of the microbeam past the pull-in threshold.     

滚珠丝杠副滚珠循环系统的动力学研究和仿真

研究滚珠丝杠副的滚珠循环系统中的碰撞接触现象,根据赫兹接触理论和经典碰撞理论,并考虑滚珠和导珠管的几何外形、丝杠的转动速度等因素,建立滚珠和导珠管碰撞接触的动力学模型。在此基础上分析了滚珠的入口速度、材料密度对碰撞力大小、接触时间的影响。应用多体动力学软件Adams,根据实际物理参数,创建了导珠管和滚珠的几何模型,对钢珠在导珠管中的运动情况进行仿真模拟,获得了碰撞过程中滚珠的运动轨迹、速度、加速度以及碰撞力的变化情况。通过对不同参数的物理模型理论计算和仿真,分析了影响滚珠循环系统动力学的主要因素。理论计算和仿真、试验结果吻合较好,这对于优化导珠管结构,研究开发新型滚珠丝杠副有重要的意义。     

ROBUST EXPLICIT COMPUTATIONAL DEVELOPMENTS AND SOLUTION STRATEGIES FOR IMPACT PROBLEMS INVOLVING FRICTION

New explicit dynamic computational developments in conjunction with finite element formulations for impact problems are described in this paper. The proposed methodology is based on employing a variational inequality for dynamic problems involving Coulomb friction with the so-called forward incremental displacement–central difference method specially formulated in this paper for this class of problems. To enforce the constraints on the contact boundary, a linear complementary equation is established by means of a minimization problem subjected to constraints, which is equivalent to discretization of the variational inequality of the dynamic problem. In conjunction with these developments, a new conjugate gradient based explicit solution strategy is described for effectively solving the linear complementary equations. With the motivation for providing effective computational procedures suitable for vectorization and parallel computations, the proposed developments not only provide a fundamentally sound and robust theoretical basis but also serve to be ideally suited for impact problems involving frictional contact on high speed computing environments.     

The solution of large displacement frictionless contact problems using a sequence of linear complementarity problems

A Newton method for solution of frictionless contact problems is presented. A finite element discretization is performed and the contact constraints are given as complementarity conditions. The resulting equations, which represent the equilibrium of the system, are formulated as a generalized equation. Generalized equations, from the discipline of Mathematical Programming, are a way of writing multi-valued relations, such as complementarity conditions, in a way that is similar to ordinary equations. Newton's method is then used, in a straightforward way, to solve the present non-linear generalized equation, resulting in a sequence of Linear Complementarity Problems (LCP's).