柔性多体系统接触/碰撞动力学的若干关键问题

归纳了柔性多体系统接触/碰撞动力学中的4个关键问题: 接触区域的处理方法、 接触作用的力学模型、 柔性体的运动学描述和约束问题的数值方法. 针对这4个问题, 综述了柔性多体领域和有限元领域的现有方法, 指出了这些方法的优点和不足. 进一步提出了柔性多体系统接触/碰撞问题的发展趋势.     

基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究

基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究. 首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模, 在碰撞时采用冲量动量法求出跳跃速度, 其次在法向上引入接触约束求解出碰撞力, 在切向上采用LuGre摩擦模型分两种方式求解摩擦力, 第一种是在滑动时摩擦力由摩擦系数和碰撞力计算得出, 黏滞状态下引入切向约束计算拉格朗日乘子反应实际摩擦力, 根据黏滞/滑动切换判断计算出碰撞过程摩擦力(与Coulomb摩擦模型计算摩擦力一致); 第二种根据LuGre摩擦模型摩擦系数和法向碰撞力计算其摩擦力, 从而在碰撞时无需黏滞/滑动切换, 采用相同的摩擦力计算公式. 通过与Coulomb摩擦模型对比发现, LuGre摩擦模型描述碰撞切向摩擦过程更精确, LuGre摩擦模型黏滞时建立约束方程和碰撞采用统一的摩擦力公式这两种建模方式描述的斜碰撞动力学特性没有区别, 进而说明采用法向接触约束和LuGre摩擦模型具有满足碰撞非嵌入情况、避免黏滞/滑动切换、描述摩擦力相对准确的优势.      

平面柔性多体碰撞阶段附加接触约束方法

含碰撞现象的柔性多体动力学涵盖碰撞前、碰撞中和碰撞后3个不同拓扑的过程, 针对这个特点, 采用附加接触约束方法可将上述3个过程的动力学方程形式统一. 引入碰撞检测机制, 实现拓扑模型的自动变化. 与传统的罚函数方法不同, 以物体间互不嵌入的思想建立附加接触约束, 计算碰撞期间的动力学过程. 通过对发生多次碰撞问题的仿真,从兼顾计算精度和计算效率的角度, 对提出的附加接触约束方法和LS-DYNA罚函数方法进行了对比, 改进了LS-DYNA罚函数方法存在的不足.      

作大范围回转运动柔性梁斜碰撞动力学研究

为正确估计由于碰撞引起的多柔体系统动力学特性的变化,针对作大范围回转运动的柔性梁与一固定斜面发生斜碰撞的情况,在考虑刚柔耦合效应的多柔体系统动力学建模理论的基础上,利用假设模态法建立起重力场作用下的柔性梁一致线性化动力法向碰撞过程中系统的动力行为。基于Ｈｅｒｔｚ接触理论和非线性阻尼项建立法向碰撞接触模型,基于线性切向接触刚度建立柔性梁切向碰撞接触模型,提出的数值算法保证了计算结果的合理性,给出的仿     

接触碰撞动力学的多变量选取方法

在柔性多体的接触碰撞动力学问题中,多变量方法基于附加约束的接触模型,将柔性体的变形用不同变量来描述：接触局部区域的变形用有限元节点坐标描述,非接触局部区域的变形用模态坐标描述,兼顾了计算精度和效率. 将该方法推广到三维空间碰撞问题,对两柔性杆纵向碰撞过程进行动力学仿真,数值结果与实验结果吻合良好,验证了该方法的有效性. 针对柔性体各自区域的变量如何选取的问题,研究了节点取法、模态阶数以及材料参数对计算结果精度的影响,寻找到合理的多变量选取方法,保证精度的同时使自由度得到最大程度的缩减.     

柔性多体系统动力学研究现状与展望

对柔性多体系统动力学的研究现状进行了概括和总结,主要从柔性体建模方法、刚柔耦合动力学、接触碰撞问题、多物理场耦合、微分代数方程求解技术、控制方法、设计优化及软件开发和实验研究等几个研究方向进行总结,并对未来的研究方向做了展望.     

多体系统动力学碰撞问题研究综述

对近年来多体系统碰撞动力学研究进展进行了评述,包括碰撞动力学建模理论、数值算法和实验方面的进展情况.根据各自不同假设条件将建模方法分为冲量动量法、连续碰撞力模型和基于连续介质力学的有限元方法,比较了各种建模方法在碰撞过程描述和数值性态方面的优势和局限性;对碰撞动力学实验在非接触式测量方面取得的最新进展进行了介绍,总结了实验对以上建模理论的验证研究,展示了实验研究方面的一些新发现.最后基于工程实际的需求提出多体系统碰撞动力学面临的新挑战.      

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.     

多体系统接触碰撞问题的牛顿-欧拉线性互补方法

基于非光滑动力学方法的多体系统接触碰撞分析是目前多体系统动力学的研究热点.本文采用牛顿-欧拉方法建立多体系统接触、碰撞问题的动力学模型,给出一种牛顿-欧拉型线性互补公式.该建模方法与目前一般采用的拉格朗日建模方法的不同之处是约束条件中除了库仑摩擦、单边约束之外还含有光滑等式约束.在建立系统动力学模型时,首先解除摩擦约束和单边约束得到原系统对应的基本系统.牛顿-欧拉方法采用最大数目坐标建立基本系统的动力学方程,由于坐标不相互独立,因此基本系统中带有等式约束,其数学模型为一组微分代数方程.借助约束雅可比矩阵,在基本系统微分代数方程中添加摩擦接触和单边约束对应的拉氏乘子,就可以得到系统全局运动的具有变拓扑结构特征的动力学方程,再结合非光滑约束互补条件便可构成完备的系统动力学模型.完备的动力学模型由动力学微分方程以及等式约束和不等式约束组成.线性互补公式采用分块矩阵形式进行推导,简化了推导过程.数值计算采用基于线性互补的时间步进算法.时间步进算法是目前流行的非光滑数值算法,其突出特点是可以免去数值积分中繁琐的事件检测过程,而数值积分过程中通过对线性互补问题的求解可以确定系统的触-离状态.通过对典型的曲柄滑块间隙机构进行数值分析,验证本文方法的有效性.     

柔性机械臂系统逆动力学及驱动规律的研究

研究了柔性机械臂系统的逆动力学问题及其联接铰驱规律。在柔性多体系统动力学单向递推组集建模方法的基础上,建立了树形及含闭环的柔性多体系统正逆动力学问题同时计算的等价公式。通过一空间机械臂的数值仿真,讨论了构件的柔性效应对系统的驱动力（矩）及实际运动规律的影响。     

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.     

Partition method and experimental validation for impact dynamics of flexible multibody system

The impact problem of a flexible multibody system is a non-smooth, high-transient, and strong-nonlinear dynamic process with variable boundary. How to model the contact/impact process accurately and efficiently is one of the main difficulties in many engineering applications. The numerical approaches being used widely in impact analysis are mainly from two fields: multibody system dynamics (MBS) and computational solid mechanics (CSM). Approaches based on MBS provide a more efficient yet less accurate analysis of the contact/impact problems, while approaches based on CSM are well suited for particularly high accuracy needs, yet require very high computational effort. To bridge the gap between accuracy and efficiency in the dynamic simulation of a flexible multibody system with contacts/impacts, a partition method is presented considering that the contact body is divided into two parts, an impact region and a non-impact region. The impact region is modeled using the finite element method to guarantee the local accuracy, while the non-impact region is modeled using the modal reduction approach to raise the global efficiency. A three-dimensional rod-plate impact experiment is designed and performed to validate the numerical results. The principle for how to partition the contact bodies is proposed: the maximum radius of the impact region can be estimated by an analytical method, and the modal truncation orders of the non-impact region can be estimated by the highest frequency of the signal measured. The simulation results using the presented method are in good agreement with the experimental results. It shows that this method is an effective formulation considering both accuracy and efficiency. Moreover, a more complicated multibody impact problem of a crank slider mechanism is investigated to strengthen this conclusion.     

带约束非线性多体系统动力学方程数值分析方法

Lagrange方法是建立带约束多体系统动力学方程的普遍方法之一 ,其方程的形式为微分 代数方程组 ,数值计算与数值分析是研究多体系统动力学特性的重要方法。本文利用缩并法给出了带约束多体系统动力学方程的隐式数值计算方法和Lyapunov指数的计算方法。将数值仿真、Lya punov指数计算和Poincare映射有机结合 ,分析非线性多体系统动力学行为。通过一个算例 ,说明该方法的有效性     

Modeling intermittent contact for flexible multibody systems

This paper consists of two parts. The first part presents a complementarity based recursive scheme to model intermittent contact for flexible multibody systems. A recursive divide-and-conquer framework is used to explicitly impose the bilateral constraints in the entire system. The presented approach is an extension of the hybrid scheme for rigid multibody systems to allow for small deformations in form of local mode shapes. The normal contact and frictional complementarity conditions are formulated at position and velocity level, respectively, for each body in the system. The recursive scheme preserves the essential characteristics of the contact model and formulates a minimal size linear complementarity problem at logarithmic cost for parallel implementation. For a certain class of contact problems in flexible multibody systems, the complementarity based time-stepping scheme requires prohibitively small time-steps to retain accuracy. Modeling intermittent contact for this class of contact problems motivated the development of an iterative scheme. The second part of the paper describes this iterative scheme to model unilateral constraints for a multibody system with relatively fewer contacts. The iterative scheme does not require a traditional complementarity formulation and allows the use of any higher order integration methods. A comparison is then made between the traditional complementarity formulation and the presented iterative scheme via numerical examples.     

Contact-impact formulation for multi-body systems using component mode synthesis

The efficiency and accuracy are two most concerned issues in the modeling and simulation of multi-body systems involving contact and impact. This paper proposed a formulation based on the component mode synthesis method for planar contact problems of flexible multi-body systems. A flexible body is divided into two parts： a contact zone and an un-contact zone. For the un-contact zone, by using the fixed-interface substructure method as reference, a few low-order modal coordinates are used to replace the nodal coordinates of the nodes, and meanwhile, the nodal coordinates of the local impact region are kept unchanged, therefore the total degrees of freedom （DOFs） are greatly cut down and the computational cost of the simulation is significantly reduced. By using additional constraint method, the impact constraint equations and kinematic constraint equations are derived, and the Lagrange equations of the first kind of flexible multi-body system are obtained. The impact of an elastic beam with a fixed half disk is simulated to verify the efficiency and accuracy of this method.     

A frictional mortar contact approach for the analysis of large inelastic deformation problems

A multibody frictional mortar contact formulation (Gitterle et al., 2010) is extended for the simulation of solids undergoing finite strains with inelastic material behavior. The framework includes the modeling of finite strain inelastic deformation, the numerical treatment of frictional contact conditions and specific finite element technology. Several well-established and recent models are employed for each of these building blocks to capture the distinct physical aspects of the deformation behavior. The approach is based on a mortar formulation and the enforcement of contact constraints is realized with dual Lagrange multipliers. The introduction of nonlinear complementarity functions into the frictional contact conditions combined with the global equilibrium leads to a system of nonlinear equations, which is solved in terms of the semi-smooth Newton method. The resulting method can be interpreted as a primal–dual active set strategy (PDASS) which deals with contact nonlinearities, material and geometrical nonlinearities in one iterative scheme. The consistent linearization of all building blocks of the framework yields a robust and highly efficient approach for the analysis of metal forming problems. The effect of finite inelastic strains on the solution behavior of the PDASS method is examined in detail based on the complementarity parameters. A comprehensive set of numerical examples is presented to demonstrate the accuracy and efficiency of the approach against the traditional node-to-segment penalty contact formulation.     

基于李群局部标架的多柔体系统动力学建模与计算

多柔体系统动力学主要研究由多个具有运动学约束、存在大范围相对运动的柔性部件构成的动力学系统的建模、计算和控制.多柔体系统不仅具有柔体大变形导致的几何非线性,更具有大范围刚体运动引起的几何非线性,其非线性程度远高于计算结构力学所研究的几何非线性问题.本文基于李群局部标架(local frame of Lie group, LFLG),讨论如何发展一套新的多柔体系统动力学建模和计算方法体系, 具体内容包括:基于局部标架的梁、板壳单元,适用于长时间历程计算的多柔体系统碰撞动力学积分算法,结合区域分解技术的大规模多柔体系统动力学并行求解器, 以及若干验证性算例.上述基于李群局部标架的方法体系可在计算中消除刚体运动带来的几何非线性问题,使柔体系统的广义惯性力、广义弹性力及其雅可比矩阵满足刚体运动的不变性,使多柔体系统动力学与大变形结构力学相互统一,有望推动新一代多柔体系统动力学建模和计算软件的发展.