| Optimization Design |
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| Nonlinear modeling and optimization of single-stage compliant orthogonal displacement amplification mechanism |
| KONG Chui-wang, CHEN Wei-lin, LU Qing-hua, LUO Lu-feng, ZHANG Yun-zhi |
| School of Mechatronics Engineering, Foshan University,Foshan528000,China |
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Abstract In the field of precision engineering, it is a research hotspot to realize the flexibility and stability of operation simultaneously. Single-stage compliant orthogonal displacement amplification mechanism can realize parallel grasping by orthogonal displacement transformation, and improve the flexibility of operation through displacement amplification. However, the traditional modeling method for this mechanism is mainly based on the small deflection assumption and ignores the shearing effect, which results in a lower model precision. For this reason, the precise nonlinear modeling and optimization of typical single-stage compliant orthogonal displacement amplification mechanism with single-force input were carried out. Considering the shearing effect and geometric nonlinear factors, the output displacement of the mechanism was modeled by a two-step semi-analytical method, which realized the rapid prediction of nonlinear results. Firstly, based on the energy method and the Euler-Bernoulli beam theory, the linear elastic analytical model of the output displacement of this mechanism was established, and the shearing nonlinear correction coefficient was fitted by using the small deflection-based static finite element analysis. Secondly, combining the geometric nonlinear static finite element analysis with numerical fitting, the geometric nonlinear correction coefficient model of the output displacement of this mechanism was established. In order to maximize the output displacement and suppress the geometrical nonlinearity, a comprehensive optimization strategy for the planar dimensions and thickness of this mechanism was proposed. The effectiveness of nonlinear output displacement model and optimization results of this mechanism were verified by ANSYS Workbench finite element simulation. Simulation results showed that the errors of nonlinear output displacement model for this mechanism was smaller than 5%, and according to different optimizing strategies, the output displacement could be effectively improved, or the geometrical nonlinearity could be restricted to a designated range. The research indicates that using the proposed method to conduct the nonlinear model and optimization of the single-stage compliant orthogonal displacement amplification mechanism, the displacement output performance, open-loop controlling accuracy and real-time performance of compliant mechanism-based piezoelectric-driven microgripper can be effectively improved, which is conducive to realize the stable and smart micro-manipulation.
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Received: 20 June 2019
Published: 28 February 2020
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单级柔顺正交位移放大机构非线性建模与优化
同时实现操作的灵活性与稳定性是精密工程领域的研究热点。单级柔顺正交位移放大机构可通过正交位移转换实现平行夹持，并通过位移放大提高操作的灵活性，但该机构的传统建模方法主要基于小变形假定并忽略剪切作用，导致模型精度较低。为此，对典型的单力输入单级柔顺正交位移放大机构进行精确的非线性建模与优化。考虑到剪切作用与几何非线性因素，对单级柔顺正交位移放大机构输出位移进行两步法半解析建模，以实现非线性结果的快速预测。第1步，基于能量法与欧拉-伯努利梁理论，建立该机构输出位移的线弹性解析模型，并结合小变形静力学有限元分析，拟合剪切非线性修正系数；第2步，结合几何非线性静力学有限元分析与数值拟合，建立该机构输出位移的几何非线性修正系数模型。为最大化输出位移并抑制几何非线性作用，提出机构平面尺寸和厚度综合优化策略，并利用ANSYS Workbench有限元仿真验证了机构输出位移非线性模型与优化结果的有效性。仿真结果显示，机构输出位移非线性模型的误差小于5%，且可依据不同优化策略显著增大输出位移或将几何非线性程度约束于指定范围内。研究表明利用所提出的方法对单级柔顺正交位移放大机构进行非线性建模与优化，可有效提高压电驱动柔顺微夹钳的位移输出性能与开环控制的精度和实时性，有利于实现稳定灵活的微操作。
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