考虑弹簧阻尼作动器解析雅可比矩阵的多刚体动力学分析
发布时间：2018-09-05 21:13
【摘要】：弹簧-阻尼-作动器(spring-damper-actuator,SDA)是多体系统中常见的力元,在工程领域中有着广泛的应用.采用绝对坐标方法建立的多体系统动力学控制方程通常是复杂的非线性微分-代数方程组.为了保证数值解的精度和稳定性,通常需要采用隐式算法求解动力学方程,而雅可比矩阵的计算在隐式数值求解过程中至关重要.对于含有SDA的多体系统,SDA造成的附加雅可比矩阵是与广义坐标和广义速度相关的高度非线性函数.目前的很多研究工作专注于广义力向量的计算,然而对附加雅克比矩阵的计算则少有关注.针对含SDA的多刚体系统进行动力学分析,首先基于Newmark算法研究其在动力学方程求解中的雅可比矩阵的构成形式;然后推导SDA的广义力向量对应的附加雅可比矩阵,其中包括广义力向量对广义坐标和对广义速度的偏导数矩阵.最后通过两个数值算例研究附加雅可比矩阵对动力学分析收敛性的影响;数值分析表明:当SDA的刚度、阻尼和作动力数值较大时,SDA导致的附加雅可比矩阵对数值解的收敛性有重要影响;当考虑SDA对应的附加雅可比矩阵时,动力学分析可以以较少的迭代步实现收敛,从而减少分析时间.
[Abstract]:Spring-damping-actuator (spring-damper-actuator,SDA) is a common force element in multi-body systems and has been widely used in engineering fields. The dynamic control equations of multibody systems established by the absolute coordinate method are usually complex nonlinear differential-algebraic equations. In order to ensure the accuracy and stability of the numerical solution, implicit algorithm is usually used to solve the dynamic equation, and the Jacobian matrix is very important in the implicit numerical solution. For multibody systems with SDA, the additional Jacobian matrix is a highly nonlinear function related to generalized coordinates and generalized velocities. Many researches have focused on the computation of generalized force vectors, but little attention has been paid to the computation of additional Jacobian matrices. The dynamic analysis of multi-rigid body system with SDA is carried out. Firstly, the form of Jacobian matrix in solving dynamic equation is studied based on Newmark algorithm, and then the additional Jacobian matrix corresponding to generalized force vector of SDA is derived. It includes generalized force vector to generalized coordinate and partial derivative matrix to generalized velocity. Finally, two numerical examples are used to study the effect of the additional Jacobian matrix on the convergence of the dynamic analysis. The additional Jacobian matrix caused by damping and dynamic values has an important effect on the convergence of the numerical solution, and when the additional Jacobian matrix corresponding to SDA is considered, the dynamic analysis can achieve convergence with fewer iterative steps. As a result, the analysis time is reduced.
【作者单位】： 大连理工大学工程力学系工业装备结构分析国家重点实验室;
【基金】：国家自然科学基金(11472069,11772074,91648204) 国家重点研发计划(2016YFB0200702)资助项目
【分类号】：O313.7
，
本文编号：2225481
[Abstract]:Spring-damping-actuator (spring-damper-actuator,SDA) is a common force element in multi-body systems and has been widely used in engineering fields. The dynamic control equations of multibody systems established by the absolute coordinate method are usually complex nonlinear differential-algebraic equations. In order to ensure the accuracy and stability of the numerical solution, implicit algorithm is usually used to solve the dynamic equation, and the Jacobian matrix is very important in the implicit numerical solution. For multibody systems with SDA, the additional Jacobian matrix is a highly nonlinear function related to generalized coordinates and generalized velocities. Many researches have focused on the computation of generalized force vectors, but little attention has been paid to the computation of additional Jacobian matrices. The dynamic analysis of multi-rigid body system with SDA is carried out. Firstly, the form of Jacobian matrix in solving dynamic equation is studied based on Newmark algorithm, and then the additional Jacobian matrix corresponding to generalized force vector of SDA is derived. It includes generalized force vector to generalized coordinate and partial derivative matrix to generalized velocity. Finally, two numerical examples are used to study the effect of the additional Jacobian matrix on the convergence of the dynamic analysis. The additional Jacobian matrix caused by damping and dynamic values has an important effect on the convergence of the numerical solution, and when the additional Jacobian matrix corresponding to SDA is considered, the dynamic analysis can achieve convergence with fewer iterative steps. As a result, the analysis time is reduced.
【作者单位】： 大连理工大学工程力学系工业装备结构分析国家重点实验室;
【基金】：国家自然科学基金(11472069,11772074,91648204) 国家重点研发计划(2016YFB0200702)资助项目
【分类号】：O313.7
，
本文编号：2225481
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