Optimizing Multi-objective Topology of Compliant Mechanism of Field-artillery Rocket Loading System
-
摘要: 采用多目标拓扑优化方法研究了满足野战火箭炮装填系统工作要求的柔性机构材料分布。以实体各向正交材料惩罚函数为拓扑优化方法(SIMP方法), 采用加权系数法定义固有频率目标函数, 并应用折衷规划法定义静态刚度和动态振动频率多目标拓扑优化函数。以等效力载荷模拟空载工况, 以位移载荷模拟负载工况。通过HyperWorks进行优化, 得到了同时满足柔性机构空载刚度、负载柔度和低阶振动频率要求的拓扑结构。对优化后的柔性机构进行仿真分析, 验证了优化结果的有效性。Abstract: A multi-objective topological optimization method was used to study the material distribution of a compliant mechanism that satisfies the requirements of a field-artillery rocket loading system. The solid isotropic material with penalization was used as the topological optimization method. The weighted coefficient method was used to define the natural frequency objective function. The compromise programming method was used to define the multi-objective topology optimization function of static stiffness and dynamic vibration frequency. No-load condition is simulated with equal-force load, and load condition is simulated with displacement load. a topology that simultaneously meets the requirements of stiffness in no-load, flexibility in load and low-order vibration frequency of the compliant mechanism is obtained through the optimization with the HyperWorks. Finally, the simulation analysis of the optimized compliant mechanism is carried out, and the effectiveness of the optimization results is verified.
-
表 1 部分边界条件
工况序号 重力方向 工况序号 位移载荷/mm X Y Z X Y Z 1 0.062 0.062 1 5 7.597 7.597 -0.470 1 2 0.062 -0.062 1 6 7.597 -7.597 -0.470 1 3 -0.062 -0.062 1 7 -7.597 -7.597 -0.470 1 4 -0.062 0.062 1 8 -7.597 7.597 -0.470 1 -
[1] LIU M, ZHAN J Q, ZHU B L, et al. Topology optimization of compliant mechanism considering actual output displacement using adaptive output spring stiffness[J]. Mechanism and Machine Theory, 2020, 146: 103728, doi: 10.1016/j.mechmachtheory.2019.103728 [2] 孙楷. 基于物理规划法的柔顺机构多目标拓扑优化研究[D]. 太原: 中北大学, 2016SUN K. Multi-objective topology optimization of complaint mechanism based on physical programming[D]. Taiyuan: North University of China, 2016 (in Chinese) [3] 谢俐, 杨乐. 三平移全柔性并联机构多目标拓扑优化设计[J]. 机械设计与制造, 2017(9): 193-196 https://www.cnki.com.cn/Article/CJFDTOTAL-JSYZ201709051.htmXIE L, YANG L. Multi-objective topology optimization design for the 3-DOF translation fully compliant parallel mechanism[J]. Machinery Design & Manufacture, 2017(9): 193-196 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSYZ201709051.htm [4] WANG G, ZHU D C, LIU N, et al. Multi-objective topology optimization of a compliant parallel planar mechanism under combined load cases and constraints[J]. Micromachines, 2017, 8(9): 279, doi: 10.3390/mi8090279 [5] MICHELL A G M. LVⅢ. The limits of economy of material in frame-structure[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1904, 8(47): 589-597 doi: 10.1080/14786440409463229 [6] 左孔天. 连续体结构拓扑优化理论与应用研究[D]. 武汉: 华中科技大学, 2004ZUO K T. Research of theory and application about topology optimization of continuum structure[D]. Wuhan: Huazhong University of Science and Technology, 2014 (in Chinese) [7] HUANG G M, YANG H L, LIU M M, et al. Structural optimization design of a certain aircraft gun closed bearing band sabot based on variable density method[J]. Journal of Physics: Conference Series, 2018, 1087(4): 042062, doi: 10.1088/1742-6596/1087/4/042062 [8] 王宪杰, 张洵安. 多相材料微结构布局及宏观结构拓扑并发优化[J]. 计算力学学报, 2015, 32(6): 716-721 https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201506002.htmWANG X J, ZHANG X A. Concurrent optimization for structure topology and its periodic multiphase materials micro distribution[J]. Chinese Journal of Computational Mechanics, 2015, 32(6): 716-721 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201506002.htm [9] 谢黎明, 高双. 基于拓扑优化的刀架支架轻量化设计[J]. 机械设计与制造工程, 2019, 48(6): 15-18 doi: 10.3969/j.issn.2095-509X.2019.06.004XIE L M, GAO S. The lightweight design for tool bracket based on topology optimization[J]. Machine Design and Manufacturing Engineering, 2019, 48(6): 15-18 (in Chinese) doi: 10.3969/j.issn.2095-509X.2019.06.004 [10] LIM J, YOU C, DAYYANI I. Multi-objective topology optimization and structural analysis of periodic spaceframe structures[J]. Materials & Design, 2020, 190: 108552, doi: 10.1016/j.matdes.2020.108552 [11] 陈锦诚, 殷跃红. 基于柔性铰链的被动柔顺机构在轴孔装配中的应用研究[J]. 机电一体化, 2017, 23(8): 3-8 https://www.cnki.com.cn/Article/CJFDTOTAL-JDTH201708001.htmCHEN J C, YIN Y H. Design study and application of passive flexible mechanism based on flexuer hinge used in hole-peg assembly[J]. Mechatronics, 2017, 23(8): 3-8 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JDTH201708001.htm [12] LIU M, ZHAN J Q, ZHANG X M. Topology optimization of distributed flexure hinges with desired performance[J]. Engineering Optimization, 2020, 52(3): 405-425 doi: 10.1080/0305215X.2019.1595612 [13] ZHU B L, ZHANG X M, FATIKOW S. A multi-objective method of hinge-free compliant mechanism optimization[J]. Structural and Multidisciplinary Optimization, 2014, 49(3): 431-440 [14] LIN J Z, LUO Z, TONG L Y. A new multi-objective programming scheme for topology optimization of compliant mechanisms[J]. Structural and Multidisciplinary Optimization, 2010, 40(1-6): 241-255 [15] SIGMUND O. A 99 line topology optimization code written in Matlab[J]. Structural and Multidisciplinary Optimization, 2001, 21(2): 120-127, doi: 10.1007/s001580050176 [16] 王春会. 连续体结构拓扑优化设计[D]. 西安: 西北工业大学, 2005WANG C H. Design for topology optimization of continuum structures[D]. Xi'an: Northwestern Polytechnical University, 2005 (in Chinese) [17] 陈垂福, 杨晓翔. 连续体结构拓扑优化敏度修正方法研究[J]. 机械设计与研究, 2017, 33(2): 104-107, 112 https://www.cnki.com.cn/Article/CJFDTOTAL-JSYY201702031.htmCHEN C F, YANG X X. Research on sensitivity modifying method of continuum topology optimization[J]. Machine Design & Research, 2017, 33(2): 104-107, 112 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSYY201702031.htm [18] 洪清泉, 赵康, 张攀, 等. HyperWorks进阶教程系列: OptiStruct & HyperStudy理论基础与工程应用[M]. 北京: 机械工业出版社, 2012HONG Q Q, ZHAO K, ZHANG P et al. OptiStruct & HyperStudy theory foundation and engineering application[M]. Beijing: Machinery Industry Press, 2012 (in Chinese) [19] MARLER R T, ARORA J S. Survey of multi-objective optimization methods for engineering[J]. Structural and Multidisciplinary Optimization, 2004, 26(6): 369-395 [20] 闻邦椿. 机械设计手册[M]. 5版. 北京: 机械工业出版社, 2012WEN B C. Manual of mechanical design[M]. 5th ed. Beijing: Machinery Industry Press, 2012 (in Chinese) [21] HUANG X, XIE Y M. Topology optimization of nonlinear structures under displacement loading[J]. Engineering Structures, 2008, 30(7): 2057-2068