• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2017, Vol. 53 ›› Issue (9): 46-57.doi: 10.3901/JME.2017.09.046

• • 上一篇    下一篇

考虑材料和几何构型的环形柔性铰链优化设计

曹玉岩, 王志臣, 周超, 王文攀   

  1. 中国科学院长春光学精密机械与物理研究所 长春 130033
  • 出版日期:2017-05-05 发布日期:2017-05-05
  • 作者简介:

    曹玉岩,男,1986年出生,助理研究员。主要研究方向为柔性结构、有限元理论。

    E-mail:yuyan_cao@126.com

Optimization of Circular-axis Flexure Hinge by Considering Material Selection and Geometrical Configuration Simultaneously

CAO Yuyan, WANG Zhichen, ZHOU Chao, WANG Wenpan   

  1. Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033
  • Online:2017-05-05 Published:2017-05-05

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。

关键词: 几何构型, 离散优化, 连续优化, 虚功原理, 柔性铰链, 复合钎料 C/C复合材料 TiAl合金 钎焊 界面结构 力学性能

Abstract:

:The circular-axis flexure hinge has been widely used in various fields. In order to solve the problem of optimizing material and geometrical configuration of flexure hinge simultaneously, the mechanical modeling method and optimization algorithm is investigated. According to the structural property of the flexure hinge, which consists of several flexural elements, the flexure hinge is simplified to indeterminate beam. The radical and tangential stiffness is derived by using virtual work principle. The whole stiffness of the flexure hinge, which is the function of material, geometrical parameters and its configuration, is obtained based on force equilibrium condition and compatible deformation. The optimization model for flexure hinge design is established. By introducing the SIMP/RAMP based model, the material parameter is expressed as the combination of artificial variables and candidate material parameters and the stiffness of flexure hinge is expressed as the combination of artificial variables and stiffness parameter corresponding to different geometrical configuration. The discrete integer programming problem can be transformed into continuous parameters optimization problem, then the gradient based method can be used to solve the optimization problem, which decreases the complexity of optimization model and improves the computational efficiency. The stiffness model of flexure hinge is verified by experiment, and the theoretical results are in good agreement with experimental results. In addition, the example of spherical mirror is given to verify the optimization model and algorithm. The obtained results show that the solving scheme guarantees the enough solution space in the beginning and finally drives the artificial variables to 0-1 values as the penal factor increasing. The surface precision of the mirror is increased by 15% after optimization design.

Key words: continuous optimization, discrete optimization, geometrical configuration, virtual work principle, flexure hinge