應用拓樸最佳化技術於負剛性系統之設計

Negative-stiffness-mechanism Design Using Topology Optimization

郭育昕(Kuo, Yu Hsin)

指導教授 ： 鄭志鈞

國立中正大學/工學院/機械工程學系/碩士(2014年)

摘要

本研究提出一以拓樸最佳化設計負剛性隔振系統的方法。建構負剛性隔振系統時，最重要的議題莫過於設計剛性調整器。本研究以拓樸最佳化決定的剛性調整器可視為一種撓性機構，固此篇研究的重點在於如何拓樸出符合目標剛性的撓性調整器。本研究之拓樸最佳化程式以 Matlab® 程式語言撰寫，輔以二維四節點之線性平面應力元素的有限元素分析模型。材料分配上採用 SIMP 法搭配 CAMD 法，再透過 MMA 與延續法最佳化拓樸結果。本研究雖在最後無法達成理想的剛性調整器，但仍證實可透過此法獲得一維線性剛性特性的拓樸結構。研究中也發現，額外的限制項或許可使最佳化迴圈中的拓樸變化更為平順。希望未來在加入幾何非線性有限元素分析模型及提供合適的限制項後，可成功最佳化預壓式負剛性隔振系統的拓樸構型。

關鍵字

負剛性機構 ； 隔振系統 ； SIMP ； CAMD ； 預壓力 ； 拓樸最佳化方法

並列摘要

A method based on topology optimization for designing a negative-stiffness-mechanism vibration protecting system (NSMVPS) is proposed. When establishing NSMVPS, the most important issue is to design the stiffness corrector. The stiffness corrector is deemed as a compliant mechanism with its layout determined by topology optimization. That is, how to determine the topology layout of the stiffness corrector with prescribed stiffness is the focus of this thesis. The finite element method with 4-node 2-D plane stress elements is adopted and programmed using Matlab® in analyzing the topology layout of the stiffness corrector during the optimization procedure. The material distribution in topology optimization is determined using SIMP and CAMD and optimized the topology by MMA with continuation method. Although the result did not reveal the ideal stiffness corrector, an one-dimension linear stiffness structural topology has been proven could be obtained by the proposed method. This research also figured out that additional constraints might helpful for smoothing the topology during the optimization iteration. The geometric non-linear FEA with appropriate constraints that aims to find the topology layout for pre-stressed NSMVPS will be introduced in the future.

並列關鍵字

Negative stiffness mechanism ； Vibration protecting system ； CAMD ； SIMP ； Pre-load ； Topology optimization

參考文獻

[1] 黃弘竣，2012，「滾珠螺桿進給系統預壓偵測技術之研發」，機械工程所碩士論文，國立中正大學。

[2] 陳宗佑，2012，「切削顫振穩定區域之預估與分析」，機械工程所碩士論文，國立中正大學。

[6] 林英帆，2012，「應用音圈馬達於負剛性系統之研發」，機械工程所碩士論文，國立中正大學。

[10] L. L. Howell, 2013, “Compliant Mechanisms,” 21st Century Kinematics, Springer, pp. 189-216.

[11] D. L. Platus, 1991, “Negative-stiffness-mechanism vibration isolation systems,” Vibration Control in Microelectronics, Optics and Metrology, San Jose, CA, Proc. SPIE 1619, pp. 44-54.