柔性机械臂模型非约束模态降维绝对误差准则

Absolute Error Selection Criteria of Unconstrained Mode for Flexible Manipulator Dynamics Model Dimension Reduction

描述柔性结构振动的非约束模态展开方法仅考虑结构参数而不考虑外部作用力,当外部驱动力频率与非约束模态的某几阶频率相等或者相近时,这样的处理将影响动力学响应的近似精度。针对此问题,且考虑到任意驱动力都可以用傅里叶分析的方法将其等效为无穷多个正弦力的叠加,提出了一种正弦力作用下基于非约束模态降维的绝对误差准则。采用有限元法描述柔性机械臂的弹性变形,应用拉格朗日法建立其动力学方程,并用非约束模态降维模型与其作对比,仿真验证了所提出的非约束模态选取准则的正确性。

The unconstrained mode dynamics dimension reduction methods only consider the structural parameters without analyzing the impact of the control force. Due to any control force can be equivalent to the superposition of an infinite number of sinusoidal force by Fourier analysis method, an unconstrained mode selection criteria under sinusoidal force based on the absolute error was presented. The elastic deformation of flexible manipulator was modeled by using the finite element （FE） method. The dynamics model of flexible manipulator was deduced by using the Lagrange approach. The solution of unconstrained mode was used for dimension reduction of the dynamics equations. The dimension reduction of the dynamics equations and the original dynamics equations were compared. Numerical simulations demonstrate the correctness of the proposed approach.