考虑材料和几何构型的环形柔性铰链优化设计

发布时间：2018-05-11 05:28

本文选题：柔性铰链 + 虚功原理　；参考：《机械工程学报》2017年09期

【摘要】：柔性铰链已广应用泛于工程中多个领域,为了解决柔性铰链材料及几何构型同时优化的问题,对铰链的力学建模方法及优化设计算法进行了深入研究。根据柔性铰链的特性,即由圆周对称分布的柔性单元组成,将柔性单元简化为超静定梁,应用虚功原理推导了柔性单元的径向及切向刚度,并根据力平衡条件及变形协调条件,推导铰链的整体刚度,该刚度为材料参数、几何参数及构型的函数。建立铰链的优化设计模型,基于SIMP/RAMP模型,将材料参数表达为人工变量与备选材料参数的组合表达式,铰链的刚度表达为人工变量与不同构型刚度的组合表达式,从而将离散混合整数规划问题转化为连续参数优化问题,使得优化模型可以采用基于梯度的优化算法求解,降低了模型复杂程度且提高了求解效率。对柔性铰链的刚度进行了试验验证,理论结果与试验结果一致。此外,以球面反射镜侧向支撑为例来验证铰链的优化设计模型及算法,结果表明:逐次增大惩罚因子的求解算法使得初始阶段具有较大求解空间,随着惩罚因子增大,人工变量最终趋于0/1值,通过铰链参数及构型优化,使反射镜面形精度较初始设计提高15%左右。
[Abstract]:Flexure hinge has been widely used in many fields in engineering. In order to solve the problem of simultaneous optimization of flexure hinge material and geometric configuration, the mechanical modeling method and optimization design algorithm of hinge are deeply studied. According to the characteristics of the flexure hinge, that is, the flexible element is composed of the circular symmetric distributed flexible element, the flexible element is simplified into a statically indeterminate beam. The radial and tangential stiffness of the flexible element is derived by the virtual work principle, and according to the force balance condition and the deformation coordination condition, The overall stiffness of hinge is derived, which is a function of material parameter, geometric parameter and configuration. The optimal design model of hinge is established. Based on SIMP/RAMP model, the material parameter is expressed as the combination expression of artificial variable and alternative material parameter, and the stiffness of hinge is expressed as combination expression of artificial variable and different configuration stiffness. Thus, the discrete mixed integer programming problem is transformed into a continuous parameter optimization problem, and the optimization model can be solved by gradient-based optimization algorithm, which reduces the complexity of the model and improves the efficiency of the solution. The stiffness of the flexure hinge is verified by experiments, and the theoretical results are in agreement with the experimental results. In addition, the optimization design model and algorithm of the hinge are verified by taking the lateral support of the spherical mirror as an example. The results show that the algorithm of increasing the penalty factor progressively makes the initial stage have a large solution space, with the increase of the penalty factor. Finally, the artificial variable tends to 0 / 1. By optimizing the hinge parameters and configuration, the precision of reflecting mirror is improved by about 15% compared with the original design.
【作者单位】：中国科学院长春光学精密机械与物理研究所;
【分类号】：TH122

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