平面整体式三自由度全柔顺并联机构拓扑优化构型设计及振动频率分析  

Configuration design with topology optimization and vibration frequency analysis for 3-DOF planar integrated fully compliant parallel mechanism

作　　者：朱大昌[1] 宋马军 

机构地区：[1]江西理工大学机电工程学院,江西赣州341000

出　　处：《振动与冲击》2016年第3期27-33,40,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(51165009);江西省自然科学基金重点项目(20142BAB206019);中国博士后科学基金(2013M541874)

摘　　要：通过建立并联原型机构的微分雅克比矩阵方程,实现平面整体式三自由度全柔顺并联机构与并联原型机构之间的矢量同构映射。在此基础上,建立平面整体式3-PRR型全柔顺并联机构SIMP(Solid Isotropic Microstructure with Penalization Method)拓扑优化模型,并采用优化准则算法,结合矢量同构映射方程,进行了平面整体式3-PRR型全柔顺并联机构同构构型设计,通过应力分布和前四阶振动固有频率仿真对比研究表明:所采取的拓扑优化设计方法使平面整体式全柔顺并联机构具有一定的均布刚度和较好的振动抑制性能,且对其振动频率的分析可为机构尺寸优化及振型优化提供了重要的依据。同时,微运动特性的仿真表明其与传统并联原型机构之间的运动学同构性一致。该结果对平面整体式全柔顺并联机构的构型拓扑优化设计有实际意义。Through establishing the differential Jacobian matrix equation of parallel prototypical mechanism, the vector isomorphic mapping between planar integrated fully compliant parallel mechanism （PIFCPM） and parallel prototypical mechanism was realized. On this basis, the solid isotropic microstructure with penalization method （SIMP） topology optimization model of a 3 - PRR type PIFCPM was built, an optimization criteria algorithm was introduced and combining with the vector isomorphic mapping equation, the isomorphic structure of the 3-PRR type PIFCPM was designed. Via a contrast simulation study on the stress distribution and first four vibration natural frequencies of the PIFCPM, it is shown that the topology optimization method introduced in the paper can achieve more uniform stiffness distribution and better performance of vibration suppression. The analysis of its vibration frequencies provides an important basis for the size and modal optimization of the mechanism. Meanwhile, the simulation regarding differential kinematical characteristics shows the kinematics isomorphism between PIFCPM and traditional parallel prototypical mechanism. The method and analysis results are helpful for structural design of PIFCPMs.

关 键 词：平面整体式三自由度全柔顺并联机构 微分矢量同构映射 拓扑优化 振动固有频率 

分 类 号：TH11[机械工程—机械设计及理论]