Dynamics Analysis of Large-Deformation Flexible Multibody Systems Based on the Adaptive Modal Selection Method
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摘要: 柔性大变形系统在进行模态降阶时，若模态选取不当，会影响求解精度甚至导致求解结果发散.对此，提出了基于绝对节点坐标法(ANCF)的柔性大变形系统模态自适应选择方法.通过ANCF梁单元建立系统的动力学模型；利用全模态稀疏表示内部区域的坐标；根据Latin超立方抽样构建采样矩阵，作用于动力学方程，以减少方程的数量；以采样后的动力学方程作为约束，构造模态坐标范数优化问题；求解优化问题可以得到具有重大贡献的模态.通过两个实例表明：数值计算结果与常用方法的结果高度吻合并且求解效率显著提升.
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关键词:
- 柔性多体动力学 /
- 自适应选择 /
- 动态响应 /
- 绝对节点坐标法(ANCF)
Abstract: During the modal truncation to reduce the model order of flexible multibody systems, the inappropriate modal selection would impair the precision of dynamic responses, or even cause divergent solutions. Thus, an efficient method of adaptive modal selection based on the absolute nodal coordinate formulation (ANCF) was proposed for large-deformation flexible multibody systems. The dynamic model for the system was established with the ANCF beam elements. The full modal sparse representation was used for the coordinates of the interior region. The sampling matrix was built through the Latin hypercube sampling to reduce the number of dynamic equations. The sparse modal coordinates' norm optimization problem was constructed with the sampling dynamic equations as constraints, to which the solution could give modes of significant contribution. Two examples show that, the numerical results are very close to the results of common methods and the computation efficiency markedly improves. -
图 1 梁部件k的初始构型和当前构型
Figure 1. Undeformed and deformed configurations of beam component k
图 5 不同时刻柔性单摆构型
Figure 5. Configurations of the free falling pendulum at different moments
图 7 提出的方法在不同时间步长下对模态的自适应选择(单摆)
Figure 7. Adaptive selection of modal coordinates with the proposed method for different time steps(pendulum)
图 8 全局坐标系下的3-RRR并联机器人示意图
Figure 8. Geometry and global coordinates of the 3-RRR mechanism
图 10 移动平台在x，y方向上的位移以及转角θ
Figure 10. Rotation angle θ and displacements in directions x and y of the platform
图 11 提出的方法在不同时间步长下对模态的自适应选择
Figure 11. Adaptive selection of modal coordinates with the proposed method for different time steps
表 1 单摆的几何与材料参数
Table 1. Geometry parameters and material parameters of the pendulum
parameter value length l/m 1 square sectional area A/m2 4×10-4 Young’s modulus E/Pa 7×105 density ρ/(kg/m3) 7.2×103 moment of inertia I/m4 1.333×10-8 
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表 2 单摆传统ANCF和所提出方法的计算效率(单位: s)
Table 2. Computation efficiency of the ANCF and the proposed method for pendulums (unit: s)
model matrix operation updated Jacobian matrix, stiffness matrix and residue etc total time ANCF 176.411 598.334 787.071 proposed 118.341 412.514 531.855
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表 3 机构的几何与材料参数
Table 3. Geometry parameters and material parameters of the mechanism
material parameter driving link passive link member length l/m thickness T/m 0.01 0.005 driving link 0.245 width W/m 0.03 0.01 passive link 0.242 Young’s modulus E/Pa 2.01×1011 7×108 moving stage 0.112 density ρ/(kg/m3) 2.7×103 2.7×103 fixed stage 0.400
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表 4 传统ANCF和所提出方法的计算效率(单位: s)
Table 4. Computation efficiency of the ANCF and the proposed method (unit: s)
model matrix operation updated Jacobian matrix, stiffness matrix and residue etc total time ANCF 566.283 6 766.148 1 390.966 proposed 184.131 223.639 421.281
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