摘 要
隨著有限元技術(shù)的快速發(fā)展，結(jié)構(gòu)優(yōu)化在航空航天、建筑、汽車、工程機(jī)械等領(lǐng)域的結(jié)構(gòu)設(shè)計(jì)方面應(yīng)用越來越廣泛。在刀具行業(yè)中，新型刀具材料不斷涌現(xiàn)，刀具的結(jié)構(gòu)也在不斷發(fā)展，目前針對(duì)刀具的結(jié)構(gòu)進(jìn)行形狀優(yōu)化和拓?fù)鋬?yōu)化還比較少。本文主要是深入研究形狀優(yōu)化、拓?fù)鋬?yōu)化基礎(chǔ)理論和關(guān)鍵技術(shù)，并成功將形狀優(yōu)化和拓?fù)鋬?yōu)化技術(shù)應(yīng)用于YT15硬質(zhì)合金可轉(zhuǎn)位車刀的設(shè)計(jì)。
深入研究了形狀優(yōu)化的數(shù)學(xué)模型、序列二次規(guī)劃算法、靈敏度分析；深入研究了基于密度法的材料插值模型、準(zhǔn)則法、數(shù)值不穩(wěn)定現(xiàn)象和解決方法。通過對(duì)YT15硬質(zhì)合金可轉(zhuǎn)位車刀進(jìn)行有限元分析，確定了形狀優(yōu)化和拓?fù)鋬?yōu)化的約束邊界條件。在形狀優(yōu)化中，確定了刀桿和刀片的形狀變量，并輸出了目標(biāo)函數(shù)和設(shè)計(jì)變量的迭代曲線和優(yōu)化結(jié)果，并做了靈敏度分析。在拓?fù)鋬?yōu)化中，分別完成了車刀二維結(jié)構(gòu)和三維結(jié)構(gòu)的拓?fù)鋬?yōu)化，輸出了迭代曲線，并對(duì)優(yōu)化結(jié)果進(jìn)行重構(gòu)和仿真驗(yàn)證。
論文主要完成了以下幾個(gè)方面的研究:
(1)闡述了形狀優(yōu)化數(shù)學(xué)模型中的三要素，深入研究形狀優(yōu)化模型的序列二次規(guī)劃算法，并完成了形狀優(yōu)化的靈敏度分析。
(2)深入研究SIMP模型和OC準(zhǔn)則法，推導(dǎo)了最大剛度優(yōu)化的迭代過程以及各參數(shù)對(duì)優(yōu)化結(jié)果的影響，探討了拓?fù)鋬?yōu)化存在的數(shù)值不穩(wěn)定現(xiàn)象和解決方法。
(3)對(duì)YT15硬質(zhì)合金可轉(zhuǎn)位車刀有限元分析，根據(jù)刀片和刀桿的應(yīng)力、位移云圖確定優(yōu)化約束條件，完成了形狀優(yōu)化設(shè)計(jì)，并輸出了目標(biāo)函數(shù)和設(shè)計(jì)變量的迭代曲線和優(yōu)化結(jié)果，通過靈敏度分析，找出了進(jìn)一步優(yōu)化的形狀變量。
(4)用兩種不同的方法完成了二維結(jié)構(gòu)的拓?fù)鋬?yōu)化，并對(duì)比發(fā)現(xiàn)結(jié)果的一致性。其次，完成了三維結(jié)構(gòu)的拓?fù)鋬?yōu)化，輸出了目標(biāo)函數(shù)和設(shè)計(jì)變量的迭代曲線，并對(duì)模型進(jìn)行重構(gòu)和驗(yàn)證。
(5)以SIMP材料插值模型和OC算法為理論基礎(chǔ)，Matlab計(jì)算工具和C#語言開發(fā)了可轉(zhuǎn)位車刀結(jié)構(gòu)優(yōu)化設(shè)計(jì)平臺(tái),完成了可轉(zhuǎn)位車刀二維結(jié)構(gòu)、三維結(jié)構(gòu)的優(yōu)化。

關(guān)鍵詞：可轉(zhuǎn)位車刀；形狀優(yōu)化；靈敏度分析；拓?fù)鋬?yōu)化；材料插值;準(zhǔn)則法；



Abstract
With the development of FEM technology, structure optimization has been applied in the aviation, building, automobile, engineering machinery and other industries more and more widely. The shape and topological optimization research based on 2 and 3 dimensional structure has been difficult and hot. This paper is mainly aimed at the shape and topological optimization of continuous body, study the fundamental theories and key technologies in-depth, and successfully applied to shape and topology optimization design on YT15 indexable turning tool.
According to the basic theory of shape optimization, described three key elements of mathematical model ,study the sequential quadratic programming algorithm in depth that solving the model from many optimization algorithm, and complete the key technology shape of optimization--sensitivity analysis.
In this paper, complete the following aspects:
（1）Described three key elements of mathematical model ,study the sequential quadratic programming algorithm in depth, and complete sensitivity analysis.
（2）Study SIMP materials interpolation model and OC criteria method in-depth，deduce the iteration process optimization of the biggest stiffness, discuss parameters on the effect of the optimization, discussed the topology optimization of the existing numerical unstable phenomenon and solutions.
（3）Finite-element analysis on YT15 hard alloy indexable turning tool , acquire optimizing constraints according to stress, displacement distribution contour of blade and toolbar and Engineering Requirement, completed the shape optimization design of indexable turning tool, output the iteration curve of target function and design variable , and complicated sensitivity analysis ,find out shape variables can be further optimized.
（4）Completed 2 dimension structure topological optimization with 2 different methods, find the consistency of the optimization results. In addition, completed the lathe tool 3 dimensional structure topological optimization, output the iteration curve of objective function and shape variables, and reconstruct the model and confirmed the result.
（5）With the basic theory of SIMP and OC Criteria Method，develop indexable turning tool design platform with the function of optimization. Completed the lathe tool 2 and 3 dimensional structure optimization.

Keywords: Indexable Turning Tool, Shape Optimization，Sensitivity Analysis , Topological Optimization, Criteria Method
目 錄
摘 要 I
ABSTRACT III
第1章 緒論 1
1.1 課題研究的背景及意義 1
1.2 結(jié)構(gòu)優(yōu)化設(shè)計(jì)的概述 2
1.3 國內(nèi)外研究現(xiàn)狀 3
1.3.1 刀具設(shè)計(jì)研究現(xiàn)狀 3
1.3.2 形狀優(yōu)化的國內(nèi)外研究現(xiàn)狀 5
1.3.3 拓?fù)鋬?yōu)化國外研究現(xiàn)狀 5
1.4 論文主要研究內(nèi)容和組織結(jié)構(gòu) 6
1.4.1 主要的研究內(nèi)容 6
1.4.2 全文的組織結(jié)構(gòu) 7
1.5 本章小結(jié) 9
第2章 形狀優(yōu)化的模型和求解 10
2.1 引言 10
2.2 形狀優(yōu)化設(shè)計(jì)的數(shù)學(xué)模型 10
2.3 形狀優(yōu)化的求解算法 12
2.3.1 形狀優(yōu)化算法 12
2.3.2 序列二次規(guī)劃法（SQP） 13
2.4 形狀優(yōu)化的靈敏度分析 15
2.5 本章小結(jié) 17
第3章 連續(xù)體結(jié)構(gòu)拓?fù)鋬?yōu)化的模型和求解 18
3.1 引言 18
3.2 密度法的SIMP材料插值模型 18
3.2.1 SIMP材料插值方法的拓?fù)鋬?yōu)化模型 19
3.2.2 多載荷工況下結(jié)構(gòu)拓?fù)鋬?yōu)化模型 22
3.2.3 基于制造工藝約束的拓?fù)鋬?yōu)化模型 24
3.3 連續(xù)體拓?fù)鋬?yōu)化SIMP模型的求解算法 24
3.3.1 ..