含非理想约束多柔体系统递推建模方法

RECURSIVE METHOD FOR MODELING FLEXIBLE MULTIBODY SYSTEMS WITH NON-IDEAL CONSTRAINTS

基于多体系统中邻接物体运动学递推关系,可以证明树状多体系统中末端物体的作用体现为传递给其内接物体的惯性和外力.由于闭环系统切断铰约束反力和非理想约束反力可看作为系统外力,任何复杂系统都可以转化为等效的树系统,并且系统约束方程中所涉及的广义加速度可以系统化地用描述约束反力的拉氏乘子替换.基于以上结果,提出了针对含非理想约束多柔体系统递推建模方法.利用该方法可以将复杂多体系统动态减缩为单个物体,从而在求解系统加速度时不需对整个系统的质量矩阵进行求逆运算,同时大幅度地降低了非理想约束反力方程的维数.通过一个算例具体说明了所提方法的求解过程,算例结果与现有商业软件所得结果一致.

With the recursive kinematics relationship between the two bodies interconnected with a joint, it is showed that the interaction between the outermost body and the inboard body in a tree-type multibody system can be measured by the transmission of the inertia mass and forces.The non-ideal constraint forces and the constraint forces at the cut-joints in a closed-loop multibody system can be viewed as external applied forces,therefore,any mutibody system corresponds to an equivalent tree-type system.Moreover,the general accelerations of the system appearing in the constraint equations can be systematically replaced by the Lagrange multipliers which are related to the constraint forces.Based on the above ideas,a recursive method is presented, by which,any closed-loop flexible multibody system with non-ideal constraints can be dynamically reduced to an equivalent system with only one body in a recursive manner.Consequently,the inverse of the mass matrix of multibody systems is not involved in the calculations of the general accelerations,and the number of equations to solve the non-ideal constraint forces can be reduced to minimum.An example is analyzed to illustrate and validate the presented method in details.