多体系统接触碰撞问题的牛顿-欧拉线性互补方法

发布时间：2018-05-25 11:03

本文选题：非光滑 + 多体系统　；参考：《力学学报》2017年05期

【摘要】：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.
[Abstract]:The contact collision analysis of multibody system based on nonsmooth dynamics method is a hot topic in the field of multibody system dynamics. In this paper, the Newton-Euler method is used to establish the dynamic model of the contact and collision problems of multi-body systems, and a Newton-Eulerian linear complementary formula is given. The difference between this method and Lagrangian modeling method is that the constraints include smooth equality constraints in addition to Coulomb friction and unilateral constraints. When the system dynamics model is established, the basic system corresponding to the original system is obtained by lifting the friction constraint and the unilateral constraint. The Newton-Euler method uses the maximum number of coordinates to establish the dynamic equations of the basic system. Because the coordinates are not independent of each other, the basic system has equality constraints, and its mathematical model is a set of differential algebraic equations. With the help of constrained Jacobian matrix and adding a Lagrangian multiplier corresponding to friction contact and unilateral constraint to the differential algebraic equation of the basic system, the dynamic equations with variable topological structure of the global motion of the system can be obtained. A complete system dynamic model can be constructed by combining the nonsmooth constraint complementary conditions. A complete dynamic model consists of dynamic differential equations, equality constraints and inequality constraints. The linear complementary formula is derived in the form of block matrix, which simplifies the derivation process. The time step algorithm based on linear complementarity is used in the numerical calculation. Time step algorithm is a popular non-smooth numerical algorithm, which can avoid the tedious event detection process in numerical integration. In the process of numerical integration, the contact-off state of the system can be determined by solving the linear complementarity problem. The effectiveness of this method is verified by numerical analysis of typical crank slider clearance mechanism.
【作者单位】：华北理工大学理学院;
【基金】：河北省自然科学基金资助项目(A2013209221)
【分类号】：O313.7

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