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北京航空航天大学学报 2018
考虑单元界面关联特性的微定位平台刚度建模
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Abstract:
摘要 设计了一种含折叠梁的并联微定位平台，具有大行程、低阻力的特点。采用传递矩阵法求解其刚度，建立各柔性子单元的传递矩阵，利用相邻单元公共结点实现传递性，通过力平衡方程、变形协调方程求解其末端位移与输入力之间的刚度矩阵，并提出了考虑全柔性的弹性折叠梁及弹性移动副刚度的求解方法。将传递矩阵法求解结果与有限元分析结果对比，误差在20.5%以内，在此基础上，考虑到模块化刚度分析方法将各子单元视为独立体，忽略各子单元之间的界面关联特性，提出了一种根据各子单元界面关联特性进行修正的方法，结果表明，该方法使其误差降低到10%以内，更好地满足了实际工程需求。
Abstract：A parallel micro-positioning platform with folded beams was designed, which has characteristics of large stroke and low resistance. Stiffness was solved by transfer matrix method. First, transfer matrix of flexible subunit was established. The transitivity characteristics became available by taking advantage of the common node belonging to adjacent elements. Finally, the stiffness matrix between input force and output displacement of flexible mechanism was solved according to the force balance equation and compatibility equation of deformation. A method to solve the stiffness of compliant folded beam and compliant prismatic pair considering full flexibility was put forward. The result of deformation error is less than 20.5% compared with finite element analysis. On this basis, this method ignored the correlation between the subunits because the modular stiffness analysis method regarded each subunit as independent. A modified method considering each subunit dependency was put forward, which reduced the error to less than 10% and made the results better meet the actual engineering needs.
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