本文選題：非光滑 + 多體系統(tǒng)��； 參考：《力學學報》2017年05期

【摘要】：基于非光滑動力學方法的多體系統(tǒng)接觸碰撞分析是目前多體系統(tǒng)動力學的研究熱點.本文采用牛頓-歐拉方法建立多體系統(tǒng)接觸、碰撞問題的動力學模型,給出一種牛頓-歐拉型線性互補公式.該建模方法與目前一般采用的拉格朗日建模方法的不同之處是約束條件中除了庫侖摩擦、單邊約束之外還含有光滑等式約束.在建立系統(tǒng)動力學模型時,首先解除摩擦約束和單邊約束得到原系統(tǒng)對應的基本系統(tǒng).牛頓-歐拉方法采用最大數(shù)目坐標建立基本系統(tǒng)的動力學方程,由于坐標不相互獨立,因此基本系統(tǒng)中帶有等式約束,其數(shù)學模型為一組微分代數(shù)方程.借助約束雅可比矩陣,在基本系統(tǒng)微分代數(shù)方程中添加摩擦接觸和單邊約束對應的拉氏乘子,就可以得到系統(tǒng)全局運動的具有變拓撲結(jié)構(gòu)特征的動力學方程,再結(jié)合非光滑約束互補條件便可構(gòu)成完備的系統(tǒng)動力學模型.完備的動力學模型由動力學微分方程以及等式約束和不等式約束組成.線性互補公式采用分塊矩陣形式進行推導,簡化了推導過程.數(shù)值計算采用基于線性互補的時間步進算法.時間步進算法是目前流行的非光滑數(shù)值算法,其突出特點是可以免去數(shù)值積分中繁瑣的事件檢測過程,而數(shù)值積分過程中通過對線性互補問題的求解可以確定系統(tǒng)的觸-離狀態(tài).通過對典型的曲柄滑塊間隙機構(gòu)進行數(shù)值分析,驗證本文方法的有效性.
[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.
【作者單位】： 華北理工大學理學院;
【基金】：河北省自然科學基金資助項目(A2013209221)
【分類號】：O313.7

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