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研究生:林昆穎
研究生(外文):Lin Kun-Ying
論文名稱:在進給速度誤差下之串並聯式工具機誤差分析與補償
論文名稱(外文):The Error Analysis and Compensation of a 3-PRS Series-Parallel Mechanism under Feed Rate Error
指導教授:蕭庭郎
指導教授(外文):Shiau Ting-Nung
學位類別:碩士
校院名稱:國立中正大學
系所名稱:機械系
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:2001
畢業學年度:89
語文別:英文
論文頁數:71
中文關鍵詞:史都華平台速度分析進給速度誤差補?v最佳化
外文關鍵詞:stewart platformvelocity analysisfeed rate errorcompensationoptimization
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在工具機邁向高速化和高精度化的過程,誤差分析與補償方法影響加工精度甚巨,因此如何建立一套完整的誤差分析理論與有效的補償方法,實為提高工具機加工精度不可或缺的研究方向。一般而言,影響工具機加工精度的誤差大致可分為以下幾種,機台本身的製造誤差、組裝誤差,及在加工過程中產生的誤差。有關加工過程中產生的誤差很多,本文將針對驅動軸進給速度誤差,先分析驅動軸進給速度與刀具頭(tool tip)速度之間的關係,然後建立進給速度具誤差下之誤差模型,瞭解進給速度誤差對刀具頭速度所造成的影響,並提出兩種最佳化的方法進行誤差補償。
在進給速度分析方面,先利用順向運動學理論導出驅動軸進給量和刀具頭位移量之間的關係式,再對其取時間微分,以求得所需之進給速度與刀具頭速度關係式,並探討不同進給速度產生的影響。在速度具誤差下的誤差分析方面,將速度誤差產生的影響轉換為位置誤差,分析在不同的進給速度規劃及誤差量下對位置誤差的影響。在誤差補償方面,採用最佳化方法,將刀具處的位置誤差以平方和的方式設成目標函數,另以驅動軸之最大進給速度與加速度為限制條件,設計變數則選定為無進給速度誤差驅動軸之加、減速時間,進行誤差補償。有關誤差補償的最佳化方法,本文採用兩種方法:(1)高斯牛頓法(Gauss-Newton Method);(2)連續二次規劃法(Sequential Quadratic Programming Method),並比較補償後的結果。
根據數值結果顯示,除了進給速度誤差的大小會影響刀具頭位置外,動平台的起始角度也會有所關連,一般來說,偏擺的角度越大,則誤差越大。此外應用本文所提供之理論求解並聯式工具機於最大進給速度、加速度限制條件下之刀具位置誤差補償,可以獲得明顯且良好的改善。同時發現,當進給速度為等速的時間越短時,所補償出來的效果越好。
In recent years, the development of machine tools trends toward high-speed feeding and high accuracy. The accuracy of machine tools is affected greatly by error analysis and compensation techniques. Therefore, it is very important to establish a complete error model and effective compensation technique. In general, the errors could be categorized into two parts. One is generated during the process of manufacturing and assembly and the other is produced during machining such as feed rate error, thermal effect, vibration and chattering etc. This study is concerned with the feed rate error, which include the analysis of the velocity of tool tip with given feed rate, the establishment of feed rate error model, as well as the compensation techniques using proposed two optimization methods.
For the feed rate analysis, the displacement equations of the tool tip under the feeds of the ball screws are first derived using the direct kinematics, and the relation between the feed rate and the velocity of the tool tip can be obtained by the differentiation of associated displacement equations. Moreover, the feed rate error can be analyzed with given different accelerated and decelerated time. The compensation with given feed rate error are investigated based on two optimization methods which are the Gauss-Newton Method and the Sequential Quadratic Programming Method. The objective function is constructed of the summation of the position error of tool tip by using the Least Square Method. The constraints are the maximum velocity and acceleration of the ball screws, and the design variables are the accelerated and decelerated time of the ball screws without feed rate error.
According to the numerical results, the position of tool tip is affected by both of the magnitude of feed rate error and the initial relative position of ball screws. The velocity error of tool tip always raises as the relative position of ball screws increases. Moreover, the moving paths of tool tip after compensation are improved with modification of the accelerated and decelerated time of the ball screws by using the proposed optimization methods.
CONTENTS
ABSTRACT i
LIST OF TABLES v
LIST OF FIGURESvi
NOMENCLATUREix
CHAPTER Page
1 INTRODUCTION 1
1-1 Motivation of Research 1
1-2 Literature Review 2
1-3 Outline 4
2 DIRECT KINEMATICS ANALYSIS 5
2-1 The Coordinate System of the 3-PRS Mechanism 5
2-2 Direct kinematics 6
2-3 Numerical Algorithm — Optimization Approach Method 9
3 THE ERROR ANALYSIS OF FEED RATE 13
3-1 The Types of Error 13
3-2 The Analysis of Feed Rate 14
3-2-1 The Velocity of Moving Platform Center 14
3-2-2 The Angular Velocity of Moving Platform 16
3-3 The Error Model of Feed Rate 20
4 THE COMPENSATION ALGORITHM 24
4-1 The Compensation Problem 24
4-2 The Methods of Optimization 26
4-2-1 Gauss-Newton Method (GN) 26
4-2-2 Sequential Quadratic Programming Method (SQP) 27
5 NUMERICAL RESULTS AND DISCUSSION 32
5-1 The Feed Rate Analysis 32
5-2 The Error Analysis of Feed Rate 34
5-3 The Compensation Problem 37
6 CONCLUDING REMARKS 67
6-1 Conclusions 67
6-2 Future Works 68
REFERENCES
REFERENCE
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