柔顺桥式位移放大机构因结构紧凑、位移放大倍数大等优点已成为精密工程领域的研究热点。针对以往研究仅在线性范围内讨论桥式位移放大机构的设计与分析的问题, 本文对典型集中柔度桥式位移放大机构进行了非线性建模与优化。考虑剪切作用与几何非线性, 通过能量法、有限单元法与数值拟合, 对机构的输入输出关系进行半解析建模, 以实现非线性结果的快速预测。为实现输出位移最大化与抑制几何非线性作用, 提出机构平面内尺寸与厚度的综合优化策略。ANSYS Workbench有限元仿真显示, 机构非线性建模误差均在5%以内且优化结果具备有效性。本文提出的两步法半解析非线性建模方法以及平面内尺寸和厚度的综合非线性优化策略对其它复杂柔顺机构的非线性结果快速预测与优化设计具有参考意义。

Due to the advantages of compact structure and large displacement amplification ratio, compliant bridge-type displacement amplification mechanism (DAM) has increasingly gained attention in the field of precision engineering. In previous reports, the design and analysis of bridge-type DAM have been limited to the linear range. In this work, nonlinear modeling and optimization of a typical lumped bridge-type DAM were investigated. Considering the shearing effect and geometrical nonlinearity, the output-input relation of the mechanism was modeled half-analytically using the energy method, finite element method, and numerical fitting, and rapid prediction of nonlinear results was realized. For maximizing the output displacement and restricting the geometrical nonlinearity, comprehensive optimization strategies of planar dimensions and thickness were proposed. ANSYS Workbench finite element simulation reveals that the error of nonlinear modeling for the mechanism is limited to 5%, and the optimal results are effective. The two-step half-analytical nonlinear modeling method and comprehensive nonlinear optimization strategies of planar dimensions and thickness proposed in this paper can be applied for the rapid prediction of nonlinear results and optimal design of other complicated compliant mechanisms.