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研究生:施智綱
研究生(外文):Chih-Kang, Shih
論文名稱:行星式輥軋機輥軋成型分析研究
論文名稱(外文):A STUDY ON THREE-ROLL PLANETARY ROLLING PROCESS
指導教授:洪景華
指導教授(外文):Chinghua Hung
學位類別:博士
校院名稱:國立交通大學
系所名稱:機械工程系
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:2002
畢業學年度:90
語文別:英文
論文頁數:123
中文關鍵詞:行星式輥軋機輥軋有限元素嚙合方程式上界限法雙流線方程式
外文關鍵詞:Three-Roll Planetary Rolling MillRollingFinite Element MethodEquation of MeshingUpper Bound SolutionDual Stream Functions
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本研究針對行星式輥軋機輥軋的過程,運用有限元素分析以及上界限法來探討棒材和管件在輥軋過程中的成型變化,以期解決行星式輥軋機在生產時工件扭曲變形的情形。模擬採用三維彈塑性有限元素分析法,首先考慮輥輪的外型,及其置放時的壓下角、偏移角等參數,並對應生產時的狀況,加入適切的邊界條件、材料性質以建立適當的行星式輥軋的模組,同時參考齒輪創成的方法,運用嚙合方程式,找出輥輪與工件之間接觸關係。在進行更進一步的模擬分析前,先利用行星式三輥輪軋延試驗機與塑性黏土進行一系列的實驗,來驗證建置完成的模擬模組的合理性。接著運用此一完成驗證的模擬模組,針對不同的輥軋工作參數來觀察棒材成型時的變形及應力、應變的分佈情形。此外,亦整合了最佳化設計的方法,針對鋼棒前端凹陷之最小化,進行了雙設計變數的初步分析。
再針對行星式輥軋機生產無縫管的成型過程進行一系列的模擬分析,探討各輥軋參數對無縫管輥軋成型的影響。同時,藉由雙流線方程式可求得管件在輥軋時材料流動的三維速度場,進而運用上界限法,求出使塑性變形所消耗總功率為最小的動可容許速度場,從中求得管件在成型過程中各點的速度以及加工的能量,並與有限元素分析所求得的結果進行比較。

This dissertation adopts the finite element method and upper bound method to analyze the deformation of a rod and a seamless tube in the three-roll planetary rolling process. The three-dimensional elastic-plastic finite element simulation was employed to analyze both the deformation characteristics of this process and the distributions of stress and strain on the steel rod. The basic geometric model of the planetary rolling mill, that considers the roll profiles and the offset angle of the rolls, was first constructed. An algorithm called “Equation of Meshing” was proposed for application during simulation, from which the initial contact conditions between rolls and workpiece were derived. Before further analyses, the planetary three-roll experimental machine was used with plasticine in a series of experiments to confirm the correctness of the simulation model. Furthermore, an optimum design method was integrated into this analysis to obtain optimal design variables to reduce the cavity depth in the leading end of milled steel rods.
The deformation of the hollow tube in the three-roll planetary rolling process was also analyzed systematically. The upper bound solution with kinematically admissible velocity fields derived from dual stream functions was applied to determine the velocity field and energy consumption of the rolling process. Results from analytical and numerical analysis were compared.

TABLE OF CONTENTS
ABSTRACT(Chinese) i
ABSTRACT(English) ii
ACKNOWLEDGMENTS iii
TABLE OF CONTENTS iv
LIST OF TABLES vii
LIST OF FIGURES viii
NOMENCLATURE xi
CHAPTER 1 INTRODUCTION 1
1.1 Rolling Process 1
1.2 Three-Roll Planetary Rolling Mill 2
1.3 Literature Review 3
1.4 Scope of the Present Study 4
CHAPTER 2 THE FINITE ELEMENT MODEL OF THREE-ROLL PLANETARY ROLLING MILL 12
2.1 Simplification of PSW Model 12
2.2 Generation of Roll Profiles 12
2.3 Contact Analysis between Roll and Workpiece 14
2.3.1 Equation of Meshing 14
2.3.2 Roll Profile and Corresponding Workpiece Profile 17
CHAPTER 3 EXPERIMENT ON PLANETARY THREE-ROLL EXPERIMENTAL MACHINE 25
3.1 Introduction 25
3.2 Planetary Three-Roll Experimental Machine 25
3.3 Experimental Procedures 26
3.3.1 Preparation of Plasticine Workpiece 26
3.3.2 Material Properties of Plasticine 27
3.3.3 Rolling Procedure 27
3.3.4 Measurements of Rolled Plasticine 28
3.4 Results and Discussion 29
3.4.1 Diameter after Deformation 29
3.4.2 Characteristics of Rolled Workpiece 29
3.4.3 Inhomogeneous Deformation of Rolled Rod 31
CHAPTER 4 THE NUMERICAL STUDY ON THREE-ROLL PLANETARY ROLLING PROCESS OF ROD 45
4.1 Introduction 45
4.2 Verification of Finite Element Model 45
4.2.1 Comparison with Literature Results 45
4.2.1.1 Simulation Model 45
4.2.1.2 Rolling Load and Exit Velocity 46
4.2.2 Comparison with Experimental Results 47
4.2.2.1 Simulation Model 47
4.2.2.2 Diameter after Deformation 47
4.2.2.3 Characteristics of the Rolled Workpiece 47
4.2.2.4 Inhomogeneous Deformation of Rolled Rod 48
4.2.3 Conclusion 48
4.3 Study on Stainless Steel 49
4.3.1 Deformation of Workpiece 49
4.3.2 Rotational Speed of Rolls 50
4.3.3 Offset Angles 50
4.3.4 Stress and Strain 51
4.4 Optimization Techniques 51
4.4.1 Object Function and Design Variables 51
4.4.2 Results and Discussion 53
CHAPTER 5 THE STUDY ON PLANETARY ROLLING PROCESS OF SEAMLESS TUBE 69
5.1 Introduction 69
5.2 Stream Function 69
5.3 Dual Stream Functions 71
5.4 Velocity Field of Tube 73
5.5 Upper Bound Approach 77
5.6 Finite Element Model 79
5.7 Results and Discussion 80
5.7.1 Results of Finite Element Analysis 80
5.7.2 Results of Upper Bound Approach 81
CHAPTER 6 CONCLUSIONS AND FUTURE WORK 94
6.1 Conclusions 94
6.2 Scope for the Further Work 96
REFERENCES 98
APPENDIX A 102
A.1 Time Step Control 102
A.2 Hourglass Mode Control 104
A.3 Determination of 105
A.4 Determination of and 106
A.5 Upper Bound Solution 107
APPENDIX B 116
PUBLICATION LIST 122
LIST OF TABLES
Table. 3.1 Configuration of experimental workpiece 33
LIST OF FIGURES
Fig. 1.1 Conversion of raw material into various shapes of steel [2] 6
Fig. 1.2 Typical arrangements of rolls [6] 7
Fig. 1.3 Layout for a continuous rod mill for rolling 2-inch billets [7] 8
Fig. 1.4 Cross section of PSW [8] 9
Fig. 1.5 Roll of PSW 10
Fig. 1.6 Operating unit of tube production [13] 11
Fig. 2.1 Projective profile of the roll on the roll’s coordinate system . 18
Fig. 2.2 Relation between coordinate system of roll and coordinate system of workpiece . 19
Fig. 2.3 Mesh system of PSW 20
Fig. 2.4 Contact between roll and workpiece 21
Fig. 2.5 The profile of typical roll and its generated workpiece 22
Fig. 2.6 Modified profile of roll and its generated profile of workpiece 23
Fig. 2.7 Profile of roll corresponded to the pre-given profile of workpiece 24
Fig. 3.1 Configuration of planetary three-roll experiment machine [17]. 34
Fig. 3.2 Roll profile of the experimental machine [17] (Unit: mm) 35
Fig. 3.3 Flow curves for white plasticine 36
Fig. 3.4 Characteristic of workpiece [16] 37
Fig. 3.5 Characteristic of end cavity [16] 38
Fig. 3.6 Diameter of rolled workpiece 39
Fig. 3.7 Rolled products 40
Fig. 3.8 Pitch length of the spiral mark 41
Fig. 3.9 Threaded angle of the spiral mark 42
Fig. 3.10 End cavity of the rolled workpiece 43
Fig. 3.11 Cavity depth on the workpiece 44
Fig. 4.1 Comparisons of rolling loads 54
Fig. 4.2 Comparisons of exit velocity 55
Fig. 4.3 Mesh system of the planetary three-roll experiment machine 56
Fig. 4.4 Final diameter of workpiece 57
Fig. 4.5 Pitch length of spiral mark 57
Fig. 4.6 Threaded angle of spiral mark 58
Fig. 4.7 Cavity length in leading end 58
Fig. 4.8 Effective stress-effective strain curve of 304L stainless steel [27] 59
Fig. 4.9 Cross section of a deforming workpiece 60
Fig. 4.10 Locus of a point on the workpiece (Unit: m) 61
Fig. 4.11 Relation between rotational speed of roll and exit velocity of workpiece 62
Fig. 4.12 Relation between rotational speed of roll and rolling load 63
Fig. 4.13 Relation between offset angle and exit velocity of workpiece 64
Fig. 4.14 Relation between offset angle and rolling load 65
Fig. 4.15 von Mises stress distribution on workpiece (Unit: Pa) 66
Fig. 4.16 Effective strain distribution on workpiece 67
Fig. 4.17 Distribution of the object function values 68
Fig. 5.1 Streamlines and stream functions [32]. 82
Fig. 5.2 Configuration of tube rolling through roll [35] 83
Fig. 5.3 Workpiece in the rolling gap 84
Fig. 5.4 Mesh system of PSW 85
Fig. 5.5 Cross section of deforming tube 86
Fig. 5.6 Configuration of deforming tube 87
Fig. 5.7 Distribution of von Mises stress on deforming tube (Unit: Pa) 88
Fig. 5.8 Distribution of effective strain on deforming tube 89
Fig. 5.9 Relation between offset angle and exit velocity of workpiece 90
Fig. 5.10 Relation between offset angle and rolling load 91
Fig. 5.11 Velocity field of roll gap 92
Fig. 5.12 Energy rate 93
Fig. A.1 Influence of time step size on maximum effective strain 112
Fig. A.2 Influence of time step size on computational time 112
Fig. A.3 Hourglass mode deformation [40] 113
Fig. A.4 Artificial energy percentage 114
Fig. A.5 Influence of hourglass factor on maximum effective strain 114
Fig. A.6 Projective profile of and on the plane. 115

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