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研究生:葉家瑞
研究生(外文):Chia-JuiYeh
論文名稱:史蒂芬生III型六連桿、一平面八連桿與空間RSCR四連桿機構添加圓柱配重的全域最佳平衡設計
論文名稱(外文):On the Global Optimum Cylindrical Counterweight Balancing of the Stephenson-III Six-Bar, a Planar Eight-Bar and the Spatial RSCR Four-Bar Linkages
指導教授:邱顯堂
指導教授(外文):Shen-Tarng Chiou
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:309
中文關鍵詞:機構平衡全域最佳設計配重自由參數
外文關鍵詞:MechanismsBalancingGlobal optimum designCounterweightFree variables
相關次數:
  • 被引用被引用:3
  • 點閱點閱:387
  • 評分評分:
  • 下載下載:50
  • 收藏至我的研究室書目清單書目收藏:0
為了能在市場上保有競爭力,機器的運轉速度常須不斷提高以降低成本提高產能。但在運轉速度不斷增快的同時,機器所產生之搖撼力及搖撼力矩也隨之增加,而所導致的振動及噪音,不僅降低其加工精度,也會減短其疲勞壽命。因此加入適當的平衡設計,以降低機器的搖撼力及搖撼力矩,而改善其動態特性,一直是重要的研究課題。
而最佳化方法常被用以進行機構的平衡設計,更有人針對平面機構的平衡設計問題,分別提出二次圓錐規劃及二次規劃模式,以期能搜尋出全域最佳平衡設計。但他們或未發現所用以建構模式的慣性參數中有部分參數,在搜尋最佳解的過程中,可以自由變動,卻不影響其結果,本文稱此類參數為自由參數;或所建構的模式不夠完善,以致對其所探討的問題,未能都搜尋得全域最佳解。因此,本研究之主要目的為先提出一系統化的模式,以分辨慣性參數中何者為自由參數;接著針對史提芬生III型平面六連桿、一平面八連桿,及RSCR空間四連桿機構,在其具固定接頭的桿上添加圓柱配重的問題,分別提出最佳平衡設計模式,以期能搜尋得其全域最佳解。
本文首先根據所提出之慣性參數變換系統,推導分別於具有固定之圓柱、旋轉、滑動或球接頭的桿上添加配重,所增生之搖撼力、搖撼力矩及輸入扭矩之分析方程式,再據以分辨慣性參數中何者為自由參數。接著針對該三型機構,在其具固定接頭的桿上添加圓柱配重的的問題分別建構最佳平衡設計模式時,首先根據所提出之自由參數判斷模式,探討其慣性參數系統中那些是自由參數;再根據圓柱配重的外緣須與固定接頭的旋轉軸相切以降低所增添之慣性矩的要求,推得相依變數與獨立設計變數間的解析關係式,接著以此兩者為基礎建構其最佳配重平衡設計模式,以期搜尋得全域最佳解。所建立之模式中,配重的密度與厚度均可由設計者根據實務上之需求而給定;而目標函數則採用權重因子將搖撼力、搖撼力矩及輸入扭矩加以組合,而得以探討三種設計問題,可比較其平衡的效果。另外,針對所有的模式,分別建立其最佳解應滿足的必要及充分條件。因此,可先用必要條件搜尋所有可能的解,再利用充分條件分辨何者為最佳解。再者,又針對所探討的問題,分別建立其非線性規劃模式,作為互相比較結果之用。
在實例中,分別以一組史提芬生III型平面六連桿、一平面八連桿,及RSCR空間四連桿機構為例,分別使用本研究所建構的最佳平衡設計模式,搜尋三種設計問題的結果;另外,先用必要條件搜尋所有可能的解,再利用充分條件分辨出最佳解;在使用非線性規劃模式搜尋結果時,先以亂數各產生100組的起始估計值,再搜尋其結果。在所有實例設計中,以本研究所提出的模式所得結果與先使用必要條件搜尋所有可能的解,再利用充分條件分辨出最佳解所得者相同;而使用非線性規劃所得的結果,也未能找到比前述結果之目標函數值更小的結果。因此,本研究認為所提出的最佳平衡設計模式,可搜尋得的最佳解為全域最佳解。

In order to satisfy the marketing competing requirements, the operation speeds of machinery need be as high as possible to augment the productivities and to lower the manufacturing costs. However, higher operating speed leads to greater shaking force and shaking moment, which induce vibration and noise, and reduce not only manufacturing precisions, but also the fatigue life. Therefore, installing appropriate balancing designs on machinery to reduce their shaking effects, so as to improve their dynamic properties, is one of important research tasks.
The optimum techniques are often applied for the balancing designs of machinery. Some researchers even tried to search the global optimum balancing designs for planar linkages by using the second-order cone programming or quadratic programming. But either because some of them did not find out parts of the inertial parameters (called free variables), they used to build the model, can be changed without affecting some of shaking effects; or due to the optimization models they developed are not good enough, they have not gotten the global optimum and practical balancing design for all the problems they investigated. Therefore, The main purposes of this research are to propose a systematic model to clarify which are the free variables among the inertial parameters, then to propose models for searching the global optimal balancing designs for the Stephenson-III planar six-bar linkages, a type of planar eight-bar linkages, and the spatial RSCR four-bar linkages with adding cylindrical counterweights on the links with fixed pivots.
Based on the inertial parameter system, firstly, the analysis models of the increased shaking force, shaking moment and driving torque due to the counterweights added on the links, which have a fixed joint of either cylindrical joint, revolute joint, prismatic joint, or spherical joint, are developed, consequently, according to the derived formulae, free variables can be clarified from the inertial parameters. Additionally, analytical formulae for determining the dependent variables are derived, to satisfy the constraints of the contours of the cylindrical counterweights should be tangential to the axes of the fixed revolute joints, so that the increased moment of inertia can be minimized. With these as the bases, the models aiming at getting global optimal balancing design are proposed. The models allow the designers to specify the density and thickness of the counterweights. The shaking force, shaking moment and driving torque are all included within the objective function with their weighting factors, so as to investigate three optimal balancing design problems, and to compare their results. For each problem, the necessary and sufficient conditions of the optimal solution are also developed. Such that all the candidate solutions can be given be solving the necessary condition, and then the sufficient condition is used to check which of these solutions are optimums. Besides, a nonlinear programming model is constructed too for each problem to compare the results.
A Stephenson-III planar six-bar linkage, a planar eight-bar linkage, and a spatial RSCR four-bar linkage are used as the examples. For each of three balancing problems of each linkage, three sets of results are gotten. The first one is found by using the proposed model for searching the global optimum balancing design. In order to get the second one, the necessary condition of the optimum is applied to get all the candidate solutions, and then they are checked by applying the sufficient condition. The third one is determined by using the nonlinear programming model. The random function is used to generate 100 sets initial estimates, then they are applied to search the solutions. Based on the results of each of three balancing problems of each linkage, both of the first and second sets have only one solutions and they are the same, furthermore there is no better solution within the third sets. Thus, it is claimed that the models proposed are able to get the global optimal balancing designs of these three linkages.

摘要 i
英文摘要 iii
致謝 v
目錄 vi
表目錄 xii
圖目錄 xvi
符號說明 xxii
第一章 前言 1
1-1 研究動機 1
1-2 文獻回顧 1
1-2-1 具區域最佳解之平衡設計 2
1-2-1-1 平面機構 2
1-2-1-2 空間機構 4
1-2-2 具全域最佳解之平衡設計 7
1-2-2-1 平面機構 7
1-2-2-2 空間機構 8
1-3 研究目的與方法 9
1-4 本文內容 10
第二章 兩平面機構之運動及動力分析 11
2-1 構型與符號介紹 11
2-2 運動分析 11
2-2-1 角位移、角速度及角加速度分析 12
2-2-2 質心位置、速度及加速度分析 16
2-3 搖撼力、搖撼力矩及輸入扭矩分析 19
2-3-1 搖撼力分析 20
2-3-2 搖撼力矩分析 20
2-3-3 輸入扭矩分析 21
2-4 實例分析 21
2-4-1 運動分析 22
2-4-2 搖撼力、搖撼力矩及輸入扭矩分析 26
2-5 本章小結 27
第三章 自由參數之判定 28
3-1 慣性參數系統 28
3-2 動力分析模式 29
3-2-1 搖撼力分析方程式 29
3-2-2 搖撼力矩分析方程式 30
3-2-3 輸入扭矩分析方程式 30
3-3 自由參數 31
3-3-1 圓柱接頭 31
3-3-1-1 旋轉接頭 38
3-3-1-2 滑動接頭 41
3-3-2 球接頭 44
3-4 本章小結 45
第四章 史提芬生III型機構之最佳平衡設計 47
4-1 動力分析模式 47
4-1-1 搖撼力分析方程式 47
4-1-2 搖撼力矩分析方程式 49
4-1-3 輸入扭矩分析方程式 50
4-2 最佳平衡設計模式 51
4-2-1 最佳設計模式 51
4-2-1-1 設計變數 51
4-2-1-1-1 自由參數 51
4-2-1-1-2 相依變數 52
4-2-1-2 目標函數 53
4-2-1-3 限制條件 55
4-2-2 最佳解之類型判斷 56
4-2-2-1 無限制條件 56
4-2-2-2 有限制條件 59
4-2-3 非線性規劃模式 60
4-2-3-1 設計變數及目標函數 60
4-2-3-2 限制條件 61
4-3 實例設計與分析 62
4-3-1 設計一 62
4-3-2 設計二 66
4-3-3 設計三 70
4-3-4 結果的討論 75
4-4 本章小結 76
第五章 平面八連桿機構之最佳平衡設計 80
5-1 動力分析模式 80
5-1-1 搖撼力分析方程式 80
5-1-2 搖撼力矩分析方程式 82
5-1-3 輸入扭矩分析方程式 83
5-2 最佳平衡設計模式 84
5-2-1 最佳設計模式 84
5-2-1-1 設計變數 84
5-2-1-1-1 自由參數 84
5-2-1-1-2 相依變數 85
5-2-1-2 目標函數 86
5-2-1-3 限制條件 87
5-2-2 最佳解之類型判斷 89
5-2-2-1 無限制條件 89
5-2-2-2 有限制條件 92
5-2-3 非線性規劃模式 93
5-2-3-1 設計變數及目標函數 93
5-2-3-2 限制條件 94
5-3 實例設計與分析 95
5-3-1 設計一 95
5-3-2 設計二 99
5-3-3 設計三 103
5-3-4 結果的討論 108
5-4 本章小結 109
第六章 空間RSCR機構之最佳平衡設計 113
6-1 動力分析模式 113
6-1-1 搖撼力分析方程式 113
6-1-2 搖撼力矩分析方程式 115
6-1-3 輸入扭矩分析方程式 116
6-2 最佳平衡設計模式 117
6-2-1 最佳設計模式 117
6-2-1-1 設計變數 118
6-2-1-1-1 自由參數 118
6-2-1-1-2 相依變數 119
6-2-1-2 目標函數 120
6-2-1-3 限制條件 122
6-2-2 最佳解之類型判斷 123
6-2-2-1 無限制條件 123
6-2-2-2 有限制條件 127
6-2-3 非線性規劃模式 129
6-2-3-1 設計變數及目標函數 129
6-2-3-2 限制條件 129
6-3 實例設計與分析 130
6-3-1 設計一 131
6-3-2 設計二 136
6-3-3 設計三 142
6-3-4 結果的討論 150
6-4 本章小結 150
第七章 結論與建議 154
參考文獻 157
附錄A 史提芬生III型機構運動及動力實例分析 164
A-1 運動分析 164
A-2 搖撼力、搖撼力矩及輸入扭矩分析 167
附錄B 時變函數向量 169
B-1 扇形配重於圓柱接頭 169
B-1-1 搖撼力 170
B-1-2 搖撼力矩 170
B-1-3 輸入扭矩 172
B-2 扇形配重於旋轉接頭 172
B-2-1 搖撼力 173
B-2-2 搖撼力矩 173
B-2-3 輸入扭矩 174
B-3 球配重於球接頭 174
B-3-1 搖撼力 174
B-3-2 搖撼力矩 180
B-3-3 輸入扭矩 224
B-4 圓柱配重於球接頭 230
B-4-1 搖撼力 230
B-4-2 搖撼力矩 230
B-4-3 輸入扭矩 275
附錄C 平衡指標 282
C-1 空間機構 282
C-2 平面機構 285
附錄D 空間RSCR機構的運動及動力分析 287
D-1 構型介紹與符號定義 287
D-2 坐標轉換矩陣 288
D-3 運動分析 293
D-3-1 角位移、角速度及角加速度分析 293
D-3-2 質心位置、速度及加速度分析 296
D-4 搖撼力、搖撼力矩及輸入扭矩分析 299
D-4-1 搖撼力分析 299
D-4-2 搖撼力矩分析 301
D-4-3 輸入扭矩分析 302
D-5 實例分析 303
D-5-1 運動分析 303
D-5-2 搖撼力、搖撼力矩及輸入扭矩分析 306
D-6 本章小結 307
著作權聲明 309


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