Topology Optimization of Compliant Mechanisms Based on Rotation Constraint Strategy

doi:10.3901/JME.2023.01.082

Abstract

Abstract: Compliant mechanisms have a great application potential in ultra-precision MEMS(Micro-Electro Mechanical System) of aerospace, biomedical, bionic robot and other high-tech fields. At present, topology optimization is one of the main methods in configuration design of compliant mechanisms. In order to solve the problem of de facto hinges in the traditional topology optimization of compliant mechanisms, firstly, the rotation angle is introduced into the configuration design of the compliant mechanism. Then, the causes of the emergence of de facto hinges in the optimum results obtained by topology optimization are analyzed by taking the rotation angle as the observation. Secondly, the topology optimization model of hinge-free compliant mechanisms is established by limiting the average of squared rotation within the design domain to the allowable value, and the corresponding sensitivity analysis formulas are derived by the adjoint method. Finally, the feasibility and effectiveness of the proposed optimization model are verified by topology optimization of two classical examples, namely reverse displacement mechanism and flexible clamp. The results show that hinge-free compliant mechanisms with truss-like configuration obtained by the rotation constraint strategy exhibit a certain degree of reduction in the input displacement and output displacement, but the problems of excessive local strain and stress concentration are avoided.

Key words: compliant mechanism, topology optimization, de facto hinge, rotation, hinge-free

CLC Number:

QIAO Heting, WU Shuangshuang, YAN Ming, TANG Henan, CAI Gaoyuan. Topology Optimization of Compliant Mechanisms Based on Rotation Constraint Strategy[J]. Journal of Mechanical Engineering, 2023, 59(1): 82-90.

References

[1] ANANTHASURESH G K, KOTA S. Designing compliant mechanism[J]. Mechanical Engineering, 1995, 117(11):93-96.
[2] LEE E, GEA H C. A strain based topology optimization method for compliant mechanism design[J]. Structural and Multidisciplinary Optimization, 2014, 49(2):199-207.
[3] WANG X, LUO Z, GENG X. Experimental verification of robust topology optimization for compliant mechanism[J]. Rapid Prototyping Journal, 2020, 26(9):1485-1502.
[4] ZHANG X, ZHU B. Topology optimization of compliant mechanisms[M]. Singapore:Springer, 2018.
[5] 张宪民, 胡凯, 王念峰, 等. 基于并行策略的多材料柔顺机构多目标拓扑优化[J]. 机械工程学报, 2016, 52(19):1-8. ZHANG Xianmin, HU Kai, WANG Nianfeng, et al. Multi-objective topology optimization of multiple materials compliant mechanisms based on parallel strategy[J]. Journal of Mechanical Engineering, 2016, 52(19):1-8.
[6] 杜义贤, 李涵钊, 谢黄海, 等. 基于序列插值模型和多重网格方法的多材料柔性机构拓扑优化[J]. 机械工程学报, 2018, 54(13):47-56. DU Yixian, LI Hanzhao, XIE Huanghai, et al. Topology optimization of multiple materials compliant mechanisms based on sequence interpolation model and multigrid method[J]. Journal of Mechanical Engineering, 2018, 54(13):47-56.
[7] 朱本亮, 张宪民, 李海, 等. 基于节点密度插值的多材料柔顺机构拓扑优化[J]. 机械工程学报, 2021, 57(15):53-61. ZHU Benliang, ZHANG Xianmin, LI Hai, et al. Topology optimization of multi-material compliant mechanisms using node-density interpolation scheme[J]. Journal of Mechanical Engineering, 2021, 57(15):53-61.
[8] 占金青, 刘天舒, 刘敏, 等. 考虑疲劳性能的柔顺机构拓扑优化设计[J]. 机械工程学报, 2021, 57(3):59-68. ZHAN Jinqing, LIU Tianshu, LIU Min, et al. Topological design of compliant mechanisms considering fatigue constraints[J]. Journal of Mechanical Engineering, 2021, 57(3):59-68.
[9] YOON G H, KIM Y Y, BENDSQE M P, et al. Hinge-free topology optimization with embedded translation-invariant differentiate wavelet shrinkage[J]. Structural and Multidisciplinary Optimization, 2004, 27(3):139-150.
[10] LUO J, ZHEN L, CHEN S, et al. A new level set method for systematic design of hinge-free compliant mechanisms[J]. Computer Method in Applied Mechanics and Engineering, 2008, 198(2):318-331.
[11] ZHAN J, YANG K, HUANG Z. Topological design of hinge-free compliant mechanisms using the node design variables method[C]//International Conference on Intelligent Robotics and Applications. Springer:Cham, 2014:567-575.
[12] LUO Z, CHEN L, YANG J, et al. Compliant mechanism design using multi-objective topology optimization scheme of continuum structures[J]. Structural and Multidisciplinary Optimization, 2005, 30(2):142-154.
[13] ZHU B, ZHANG X, ZHANG Q, et al. Topology optimization of hinge-free compliant mechanisms using a two-step FEA method[C]//2013 International Conference on Manipulation, Manufacturing and Measurement on the Nanoscale. IEEE, 2013:49-54.
[14] KRISHNAKUMAR A, SURESH K. Hinge-free compliant mechanism design via the topological level-set[J]. Journal of Mechanical Design, 2015, 137(3), 031406.1-031406.10.
[15] LI Y, HUANG X, XIE Y M, et al. Evolutionary topology optimization of hinge-free compliant mechanisms[J]. International Journal of Mechanical Sciences, 2014, 86(1):69-75.
[16] ZHANG Y H, SANG Y, GE W J, et al. Topology optimization of compliant mechanism based on minimum manufacturing constraints[C]//ASIAN MMS 2016|CCMMS 2016:Mechanism and Machine Science, 2016, 645-656.
[17] ZHAN J, LUO Y. Robust topology optimization of hinge-free compliant mechanisms with material uncertainties based on a non-probabilistic field model[J]. Frontiers of Mechanical Engineering, 2019, 14(2):201-212.
[18] JUNIOR H E, FANCELLO E A, SILVA E. Stress-constrained level set topology optimization for compliant mechanisms[J]. Computer Methods in Applied Mechanical and Engineering, 2020, 362:112777.1-112777.27.
[19] 占金青, 龙良明, 刘敏, 等. 基于最大应力约束的柔顺机构拓扑优化设计[J]. 机械工程学报, 2018, 54(23):32-38. ZHAN Jinqing, LONG Liangming, LIU Min, et al. Topological design of compliant mechanisms with maximum stress constraint[J]. Journal of Mechanical Engineering, 2018, 54(23):32-38.
[20] PEDERSEN C B W, BUHL T, SIGMUND O. Topology synthesis of large-displacement compliant mechanisms[J]. International Journal For Numerical Methods in Engineering, 2001, 50(12):2683-2705.
[21] SIGMUND O. Design of multi-physics actuators using topology optimization-Part II:Two-material structures[J]. Computer methods in applied mechanics and engineering, 2001, 190(49-50):6605-6627.
[22] SVANBERG K. The method of moving asymptotes a new method for structural optimization[J]. International Journal For Numerical Methods in Engineering, 1987, 24(2):359-373.
[23] ZIENKIEWICZ O C, TAYLOR R L. Finite element method for solid and structural mechanics[M]. Singapore:Elsevier, 2005.