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采用有限段法对做大范围运动柔性航天器建模时,针对传统方法求解计算效率低的问题,提出将有限段法与空间算子代数理论结合的高效处理方法。首先采用有限段法对柔性部件进行离散,将系统构造成为带关节柔性的多刚体系统,然后采用空间算子代数理论建立递推动力学方程,保证了分段引入大量广义坐标的情况下计算量仅呈线性增长,很好地克服了分段后系统运算量急剧增长的问题。最后给出双柔性杆机械臂系统的仿真算例,分别采用空间算子代数算法(SOA)与牛顿欧拉法(NE)建模,数值仿真结果表明采用SOA法与NE法建模所得计算结果完全一致。对比两种方法计算时间表明,SOA法计算量与系统自由度呈线性关系,且远小于牛顿欧拉法,仿真结果证实了本文方法的可行性和有效性。
In the modeling of a wide range of flexible sports spacecraft using the finite-section method, aiming at the problem of low computational efficiency of the traditional method, an efficient method is proposed to combine the finite-section method with the space operator algebra theory. Firstly, the finite element method is used to discretize the flexible components, and the system is constructed as a multi-rigid body system with joint flexibility. Then the recursive dynamic equation is established by using the space operator algebra theory to ensure that the computational complexity is only large when the segment is introduced into a large number of generalized coordinates With linear growth, the problem of sharp increase of system operation after segmentation is well overcome. Finally, a simulation example of a dual-flexible-arm manipulator system is given, which are respectively modeled by SOA and Newton-Euler method (NE). The numerical simulation results show that the SOA and NE modeling results Exactly the same. Comparing the two methods shows that the computation time of SOA method is linear with the degree of freedom of the system and far less than that of Newton-Euler method. The simulation results confirm the feasibility and effectiveness of the proposed method.