臺灣博碩士論文加值系統

摘要
在精密切削中，顫振之問題一直令人困擾，之前之研究多半將時間
延遲（Time-delay）部分視為外界干擾，本研究將著重於時間延遲部分
之探討，將它確實的涵貍顙t統模式中，以期更精確的設計出控制器，
藉以達到提升切削穩定曲線的目的。首先先了解顫振之動態方程式，
將時間延遲的部分加以加入， 導出含有時間延遲的整體動態方程式，
並藉以建立整個系統方塊圖， 接著利用最佳化控制（ optimal control）
的概念， 找出含有時間延遲系統的雷卡迪方程式（ Riccati equation），
並設計最佳化控制器， 再利用電腦程式模擬其效果， 進而進行切削穩
定性分析， 以研究在含有時間延遲之最佳化控制器下， 切削穩定性的
增進程度。最後， 亦會分析無時間延遲之控制系統之切削穩定性， 做
相互的比較。以證實含有時間延遲之最佳化控制器能達到較好的切削
穩定性的增進。

ABSTRACT
Chatter is a nuisance to precision machining. Most previous
research regarded the time-delay effect in the chatter problems as a
disturbance. This research focuses on the investigation of this time-delay
problem, and considers its effect for chatter controller design. In this way,
one would achieve a better performance of improving the machining
stability. First, the time-delay effect is included in the formulation of
equations of motion for a machining process. Then the optimal control is
adopted for the system with the time-delay term, and the Riccati equation
is derived for the optimal controller. Finally the computer simulation is
conducted for verification, and the improvement on stability lobes is then
discussed.

目 錄
中文摘要------------------------------------------------------------i
英文摘要-----------------------------------------------------------ii
誌謝----------------------------------------------------------------iii
目錄----------------------------------------------------------------iv
表目錄-------------------------------------------------------------vi
圖目錄-------------------------------------------------------------vii
一、 緒論…………………………………………………………………1
1.1 研究動機………………………………………………………….1
1.2 文獻回顧………………………………………………………….2
1.3 研究目的………………………………………………………….8
1.4 本文貢獻………………………………………………………….10
1.5 本文大綱………………………………………………………….11
二、 機構刀具結構…….………………………………………………13
2.1 主動式減震器機構刀具……………………………………………13
2.1.1 主動式減震器機構刀具之結構與原理………………………13
2.1.2 主動式減震器機構刀具之運動方程式推導…………………14
2.2 懸臂樑式撓性鉸鏈機構刀具………………………………………16
2.2.1 懸臂樑式撓性鉸鏈機構刀具之原理………………………16
2.2.2 懸臂樑式撓性鉸鏈機構刀具之運動方程式推導……………18
2.3 主動式減震器機構刀具與懸臂樑式撓性鉸鏈機構刀具之比較…..…20
2.4 切削力的計算與應用………………………………………………23
v
2.4.1 主動式減震器刀具之動態方程式……………………………24
2.4.2 懸臂樑式撓性鉸鏈機構刀具之動態方程式…………………26
三、 最佳化控制理論…………………………………………………27
3.1 未含有時間延遲系統之最佳化控制理論……………………………27
3.2 含有時間延遲系統之最佳化控制理論………………………………33
四、 電腦模擬與驗證…………………………………………………39
4.1 含時間延遲之最佳化控制器………………………………………39
4.2 主動式減震器機構刀具模擬與分析…………………………………41
4.2.1 未含時間延遲之最佳化控制器………………………………43
4.2.2 含時間延遲之最佳化控制器…………………………………44
4.2.3 參數設定與電腦模擬結果……………………………………44
4.3 懸臂樑式撓性鉸鏈機構刀具模擬與分析……………………………52
4.3.1 未含時間延遲之最佳化控制器………………………………52
4.3.2 含時間延遲之最佳化控制器…………………………………53
4.3.3 參數設定與電腦模擬結果……………………………………54
五、 結論與未來展望…………………………………………………65
參考文獻..…………………………………………………………………..67
附錄一 Hamilton-Jacobi-Bellman 方程式………………………..70
附錄二 推導最佳化控制問題之必要條件……………………………..72
附錄三 求解雷卡迪方程式(Riccati Equation)…………………………..76
vi
表目錄
表2-1 兩種機構刀具比較圖表------------------------------------------------22
表4-1 主動式減震器機構刀具控制器數值表----------------------------------45
表4-2 刀具詳細規格表-------------------------------------------------------55
表4-3 Steel Alloys 材料性質--------------------------------------------------55
表4-4 懸臂樑式撓性鉸鏈機構刀具詳細規格表-------------------------------59
vii
圖目錄
圖1-1 懸臂樑式撓性鉸鏈機構刀具表示圖-------------------------------------3
圖1-2 Scott-Russell (SR)機構切削刀具表示圖---------------------------------4
圖1-3 懸臂樑式撓性鉸鏈機構刀具表示圖-------------------------------------4
圖1-4 旋轉式的搪孔切削刀具表示圖------------------------------------------5
圖1-5 切削過程之方塊圖------------------------------------------------------7
圖1-6 切削穩定曲線示意圖---------------------------------------------------8
圖1-7 研究方法流程圖--------------------------------------------------------9
圖1-8 本文大綱的簡式方塊圖--------------------------------------------11
圖2-1(a) 主動式減震器結構圖-----------------------------------------------13
圖2-1(b) 主動式減震器自由體圖--------------------------------------------14
圖2-2(a) 懸臂樑式撓性鉸鏈機構刀具結構圖--------------------------------17
圖2-2(b) 懸臂樑式撓性鉸鏈機構刀具自由體圖------------------------------17
圖4-1 未加控制器前x1-x4狀態圖---------------------------------------------40
圖4-2 x1~x4 三種狀態之變化圖-----------------------------------------------41
圖4-3 控制輸出(a)u1(b)u2 在不同的Q 值之變化圖----------------------------42
圖4-4 主動式減震器機構刀具控制方塊圖------------------------------------43
圖4-5 結構未加入控制器穩定性曲線圖--------------------------------------47
圖4-6 結構加入未含時間延遲之最佳化控制器穩定性曲線圖----------------47
圖4-7 結構加入含有時間延遲之最佳化控制器穩定性曲線圖----------------48
圖4-8 含三種情況之穩定性曲線比較圖--------------------------------------48
viii
圖4-9(a) = 108.624 c K 之位移量變化圖----------------------------------------50
圖4-9(b) = 108.624 c K 之位移量變化圖(放大6~8 秒部分)----------------------50
圖4-10(a) = 108.625 c K 之位移量變化圖--------------------------------------- 51
圖4-10(b) = 108.625 c K 之位移量變化圖(放大6~8 秒部分)--------------- ------51
圖4-11 懸臂樑式撓性鉸鏈機構刀具控制方塊圖------------------------------53
圖4-12 刀具實體圖I --------------------------------------------------------55
圖4-13 刀具設計實體圖II ---------------------------------------------------56
圖4-14 結構未加入控制器穩定性曲線圖-------------------------------------60
圖4-15 結構加入未含時間延遲之最佳化控制器穩定性曲線圖---------------61
圖4-16 結構加入含有時間延遲之最佳化控制器穩定性曲線圖---------------61
圖4-17 含三種情況之穩定性曲線比較圖-------------------------------------62
圖4-18(a) = 107.831 c K 之位移量變化圖---------------------------------------63
圖4-18(b) = 107.832 c K 之位移量變化圖-------------------------------------- 63

參考文獻
[1]. Merritt, H. E., 1965, “Theory of Self-Excited Machine-Tool Chatter,”
Journal of Engineering for Industry, pp.447-454.
[2]. Hanson, R. D., and Tsao, T-C, “Development of a Fast Tool Servo for
Variable-depth-of-cut Machining”, Proceedings of the 1994
International Mechanical Engineering Congress and Exposition,
DSC-55-2, pp. 863-871, 1994.
[3]. Rasmussen J. D., Tsao, T-C, Hanson, R.D., and Kapoor S. G., 1994,
“Dynamic variable depth of cut machining using piezoelectric
actuators”Int. J. Mach. Tools Manufact., Vol. 34, No.3, pp. 379-398.
[4]. Hanson, R. D., and Tsao, T-C, “Reducing cutting force induced bore
Cylindricity Errors by Learning Control and Variable Depth of Cut
Machining”, Journal of Manufacturing Science and Engineering,
ASME, Vol. 120, pp. 547-554, 1998.
[5]. 鄭金火, 2004, “Scott-Russell機構切削刀具之最佳化設計與分析＂,
國立高雄第一科技大學, 機械與自動化工程學系, 碩士論文.
[6]. Tewani, S. G., Switzer, T. C., Walcott, B. L., Rouch, K. E., and Massa,
T. R., 1993,“Active Control of Machine Tool Chatter for a Boring Bar:
Experimental Result,”Vibration and Control of Mechanical Systems,
ASME, Design Engineering Division(Publication) DE Vol. 61, pp.
103-115.
[7]. Tewani, S.G., Rough,K.E., Walcott, B. L.,1995, “A Study of Cutting
Process Stability of A Boring Bar With Active Dynamic Absorber”, Int.
J. Mach. Tools Manufact., Vol. 35, No.1, pp. 91-108.
[8]. Tewani, S.G., Rough,K.E., Walcott, B. L.,1991, “Active Optimal
Vibration Control using Dynamic Absorber”, Proceedings - IEEE
International Conference on Robotics and Automation, v2, p1182-1187
[9]. Tewani, S.G., Rough,K.E., Marra,M.A., Walcott, B. L.,1995,
“Vibration Control for Machining using ∞ H Techniques”, Conference
68
Proceedings - IEEE SOUTHEASTCON, p 436-442
[10]. Tewani, S.G., Rough,K.E., Marra,M.A., Walcott, B. L.,1995, “ ∞ H
Vibration Control for Machining Using Active Dynamic Absorber
Technology”, Proceedings of the American Control Conference, v 1, p
739-743
[11]. Byung-Kwon Min, George O’Neal, Yoram Koren, Zbigniew Pasek,
2002, “A smart boring tool for process control”, Mechatronics, Vol. 12,
pp. 1097-1114.
[12]. Nasab, Tarek M.M. (Saudi Oger), 1999, “Application of Smith
prediction technique in designing of variable structure control systems
for plants with time delay,” Source: IEEE International Symposium on
Industrial Electronics, Vol. 3, pp. 1111-1116.
[13]. Morioka, H.; Sabanovic, A.; Uchibori, A.; Wada, K.; Oka, M.,
June 2001, “Application of time-delay-control in variable structure
motion control systems,”Industrial Electronics, 2001. Proceedings.
ISIE 2001. IEEE International Symposium on , Vol. 2 , 12-16, pp.
1313 – 1318.
[14]. Jian-Xin Xu; Wen-Jun Cao, Dec. 2000, “Synthesized sliding mode and
time-delay control for a class of matched and unmatched uncertain
systems,” Decision and Control, 2000. Proceedings of the 39th IEEE
Conference on , Vol. 3 , 12-15 pp. 2609 – 2614.
[15]. Park, Jong Hyeon (Hanyang Univ); Kim, You Moo; Yim, Jong
Guk ,”Time-delay sliding mode control for a servo”,IEEE/ASME
International Conference on Advanced Intelligent Mechatronics, AIM,
1997, p 147
[16]. Soliman, E. (Univ of Waterloo); Ismail, F., “Chatter suppression by
adaptive speed modulation”, International Journal of Machine Tools &
Manufacture, v 37, n 3, Mar, 1997, p 355-369
[17]. Yu, Fang-Ming (Department of Electrical Engineering, National
Central University); Chung, Hung-Yuan; Chen, Shi-Yuan, Dec 1, 2003,
“Fuzzy sliding mode controller design for uncertain time-delayed
systems with nonlinear input,” Fuzzy Sets and Systems, Vol. 140, No.2,
pp. 359-374.
69
[18]. Jingchuan Pan, Chun-Yi Su, 2001, “Chatter suppression with adaptive
control in turning metal via application of piezoactuator”,Decision and
Control. Proceedings of the 40th IEEE conference on, Vol. 3, 4-7, pp.
2436-2441.
[19]. D. W. Ross, 1967, “Optimal Control of Systems Described by
Differential-Difference Equations”,Ph.D. Dissertation, Department of
Electrical Engineering, Stanford University, America.
[20]. Donald E. Kirk ,1970, “Optimal Control Theory”, Prentice-Hall.
[21]. J.M. Paros, L. Weisbord, 1965, “How to Design Flexure
Hinges”,machine design, Vol.37, No.27, pp.151-156.
[22]. Brian D. O. Anderson, John B. Moore, “Optimal Control Linear
Quadratic Methods”, Prentice-Hall.
[23]. Frank L. Lewis, Vassilis L. Syrmos, “Optimal Control”, John Wiley &
Sons, Inc.
[24]. Arthur E. Bryson, Jr., Yu-Chi Ho, “Applied Optimal Control”,Taylor
& Francis.