基于传递矩阵法的柔性杠杆放大机构刚度分析

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

Stiffness is an important performance index for the dynamic performance and positioning precision of compliant micromanipulator.Concept of transfer matrix in engineering was applied to the stiffness analysis 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 deformation 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 analysis is improved effectively,and important theoretical basis is provided for parameter design.