基于传递矩阵法的柔性杠杆放大机构刚度分析  

Stiffness analysis of a flexible lever magnifying mechanism based on transfer matrix method

作　　者：郑洋洋[1] 宫金良[1] 张彦斐[1] ZHENG Yangyang GONG Jinliang ZHANG Yanfei(School of Mechanical Engineering, Shandong University of Technology, Zibo 255049, Chin)

机构地区：[1]山东理工大学机械工程学院,淄博255049

出　　处：《北京航空航天大学学报》2017年第4期849-856,共8页Journal of Beijing University of Aeronautics and Astronautics

基　　金：国家自然科学基金(61303006);山东省优秀中青年科学家科研奖励基金(BS2012ZZ009);山东理工大学青年教师发展支持计划(2013-02)~~

摘　　要：刚度是影响柔性微动机构动态性能和定位精度的重要指标。将工程中的传递矩阵概念引入到刚度分析中,首先根据结构特点将柔性微动机构模块化并将各子单元视为柔性体,全面考虑其轴向、剪切和弯曲等变形,求解各子单元柔性体的传递矩阵,然后通过传递矩阵将各子单元组合,最后根据力平衡建立柔性微动机构输入力和输出位移之间的关系模型。研究结果表明,传递矩阵法由于考虑了各单元的多维度真实变形,因此保证了结果的高精度。同时分析过程不需要求解刚柔单元变形协调方程,而且避免了微动机构全局坐标系的转换,减少了分析计算量。最后应用该方法建立了一种柔性杠杆放大微动机构的刚度模型,与有限元分析结果的对比误差小于6.4%,有效提高了分析精度,为参数设计提供了重要理论依据。Stiffness is an important performance index for the dynamic performance and positioning preci- sion of compliant micromanipulator. Concept of transfer matrix in engineering was applied to the stiffness anal- ysis here. First, according to its structure characteristics, the compliant micromanipulator was modularized and each unit was treated as flexible body. Taking axial, shear and bending deformation into consideration, we solved transfer matrix of the subunit. Then each unit was assembled through the transfer matrix. Finally, relational model between input force and output displacement of compliant micromanipulator was established according to the force balance. The research result indicates that because multi-dimensional real deformation of each unit was taken into consideration, high-precision result was guaranteed. At the same time, the deforma- tion compatibility equations between flexible and rigid units did not need to be solved during the analysis, and conversion of compliant micromanipulator global coordinate system was avoided. The analysis and computation time was also reduced. A kind of flexible lever magnifying mechanism stiffness model was established with this method. The error is less than 6.4% compared with the result of finite element analysis. The accuracy of anal- ysis is improved effectively, and important theoretical basis is provided for parameter design.

关 键 词：柔性微动机构 传递矩阵 柔性杠杆放大机构 刚度 有限元 

分 类 号：TH112.5[机械工程—机械设计及理论]