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研究生:張政翔
研究生(外文):Zhang, Zheng-Xiang
論文名稱:螺旋轉子的創新加工方法之研究
論文名稱(外文):Study on the Manufacturing of Screw Rotors
指導教授:馮展華馮展華引用關係
指導教授(外文):Fong, Zhang-Hua
口試委員:馮展華林榮信楊智媖王進猷李政鋼
口試委員(外文):Fong, Zhang-HuaLin, Rong-ShineYang, Chih-YingWang, Chin-yuLee, Cheng-Kang
口試日期:2015-07-24
學位類別:博士
校院名稱:國立中正大學
系所名稱:機械工程學系暨研究所
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:2015
畢業學年度:103
語文別:英文
論文頁數:152
中文關鍵詞:螺旋轉子變導程刀傾成形磨齒法有限元素混合法柔度矩陣
外文關鍵詞:screw rotorvariable pithtilt form grinding methodhybrid finite element methodcompliance matrix
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雙螺旋式真空泵之核心元件為一對由同步齒輪帶動且反向旋轉的螺旋轉子,而此螺旋轉子為維持氣密性常使用一種可形成內凹齒腹的擺線來進行設計並以成形研磨法加工,然而此類轉子因過切而無法以單一成形刀具完成加工,大大地降低效率,本文提出一新型的刀傾成形磨齒法(TFG),可解決原成形法中過切的問題,並以單一刀具完成定導程轉子的加工,更進一步地,左、右旋轉子在刀傾角只具單一旋轉方向時,皆可以用同一把成形刀具來加工,而數值範例的結果亦驗證了所提出的TFG之可行性。定導程螺旋轉子雖然能以成形法來進行加工,但變導程轉子則不能以成形法生產,因此本文提出以數值控制車床(CNC Lathe)來進行變導程轉子加工的方法,在此法中我們利用轉子的軸向線形來對車刀片的初始位置與行進軌跡來進行計算與排列,且也推導了誤差模型來進行驗證,參照數值範例的結果,進一步地驗證了本文中所提出的方法是可行的,但仍需進行實驗來確認刀具壽命與加工精度。

真空泵螺旋轉子運作時,彼此之間維持一定間隙且不接觸,其運動完全仰賴一對同步齒輪來維持,而一旦齒輪產生損壞或變形則將會造成轉子卡死(Lock-up)或干涉,因此如何決定適合工作的齒輪對,強度計算是首要考量,本文整合了混合有限元法(HFEM)與齒面接觸分析(TCA)對嚙合圓柱齒輪組的靜態接觸進行計算,而本文中的結果也與ANSYS進行了比對,本文所提出的HFEM亦可用在齒面修型量的研究上。

關鍵字:螺旋轉子,變導程,刀傾成形磨齒法,有限元素混合法,柔度矩陣



The twin-screw dry vacuum pump is widely used in low and medium-low vacuum applications. Its core element consists of a pair of rotors rotating in opposite direction on parallel axes. Usually one side of the rotor profile is a concave cycloid curve to prevent the inter-lobe leakage. Screw rotors are typically finished by the form grinding method. However, such concave rotor profile is almost impossible to grind on a conventional thread grinder by one tool due to severe undercutting and secondary enveloping problems. In this paper we propose a novel Tilt Form Grinding (TFG) method to overcome the problem of concave profile grinding. By using this proposed machine arrangement, the concave rotor profile can be ground without undercutting and secondary enveloping. Further, the right-hand and left-hand screw rotor can be manufactured by the same tool when only one rotational direction in tilt angle. Numerical examples are presented to validate the proposed TFG method. The rotor of twin-screw vacuum pump with uniform pitch can be ground by form grinding tool, but the one with variable pitch not. Thus, manufacturing the screw rotor with the variable pitch by CNC Lathes is proposed. The initial position and trajectory of turning tools and the manufactured profile error of screw rotor are derived and verified numerically. According to the simulation results, the proposed CNC turning process is feasible. However, further experiments are still required to check the tool life and machining accuracy.

The screw rotor of vacuum pump works rely on a pair of timing gears, some clearances between the rotors are required. The lock-up and interference between the rotors are caused by the gear fatigue failure. So the priority will be the calculation of contact stress of the gears. In this paper, the Hybrid Finite Element Method (HFEM) combined with the Tooth Contact Analysis (TCA) was applied to solve the static contact stress problem of the meshing cylindrical gear set. Using the examples in this study, the contact stress of the meshing gears was calculated and compared with the result of ANSYS in order to validate the proposed HFEM method. Furthermore, the proposed HFEM in this study can also be used to determine the amount of tooth surface modification.

Keywords:Screw rotor, Variable pith, Tilt form grinding method, Hybrid finite element method, Compliance matrix

中文摘要 I
ABSTRACT III
ACKNOWLEDGEMENTS(致謝) V
TABLE OF CONTENTS VI
LIST OF FIRURES IX
LIST OF TABLES XIV
NOMENCLATURE XV
CHAPTER 1 INTRODUCTION 1
1.1 RESEARCH OBJECTIVE 1
1.2 LITERATURE REVIEW 4
1.3 THESIS OUTLINE 9
CHAPTER 2 THE STUDY ON TURNING PROCESS OF THE VARIABLE-PITCH TWIN-SCREW VACUUM PUMP BY CNC LATHES 12
2.1 THE MATHEMATICAL MODEL FOR TURNING THE SCREW ROTOR OF VACUUM PUMP 12
2.1.1 The mathematical model of the tooth profile of the rotors 12
2.1.2 The mathematical model of manufacturing the rotor by turning 15
2.2 THE CURVE WITH VARIABLE PITCH OF THE SCREW ROTOR 17
2.3 THE ARRANGEMENT OF THE TURNING INSERTS 20
2.4 THE CALCULATION OF THE FINISHED ERROR 24
2.5 NUMERICAL EXAMPLES AND DISCUSSIONS 26
2.5.1 The arrangement of the insert of the rotor with uniform pitch 26
2.5.2 The arrangement of the insert of the rotor with variable pitch 27
2.5.3 The arrangement of the rotor with variable pitch by using the larger insert 29
2.6 SUMMARY 31
CHAPTER 3 A NOVEL TILT FORM GRINDING METHOD FOR THE ROTOR OF DRY VACUUM PUMP 60
3.1 MATHEMATICAL MODELS OF THE TFG METHOD 60
3.1.1 Mathematical model of the grinding wheel using the TFG method 61
3.1.2 Mathematical model of the ground rotor profile using the TFG method 65
3.2 CALCULATION OF THE MINIMUM TILT ANGLE 67
3.2.1 Conventional form grinding process without tilt angle 68
3.2.2 Minimum tilt angle to avoid undercutting and secondary enveloping 70
3.3 NUMERICAL EXAMPLES AND DISCUSSIONS 72
3.3.1 Transversal tooth profile of screw rotor is given 73
3.3.2 Axial section profile of form grinding wheel is given 75
3.3.3 Left and right rotors are ground by the same form grinding wheel 77
3.4 SUMMARY 79
CHAPTER 4 CONCLUSION AND FURTHER WORKS 97
4.1 CONCLUSION 97
4.2 FURTHER WORKS 99
APPENDIX A A STUDY OF THE CONTACT STRESS ANALYSIS OF CYLINDRICAL GEARS USING THE HYBRID FINITE ELEMENT METHOD 100
A.1 MATHEMATICAL MODEL OF THE GEARS 101
A.2 THE HYBRID FINITE ELEMENT METHOD (HFEM) 101
A.2.1 Basic Assumptions 103
A.2.2 Deformation compatibility and contact status decision condition 104
A.2.3 Relative separation and continuity equations of contact pairs 106
A.2.4 Solving the spur gear contact problem by the hybrid finite element method (HFEM) with tooth contact analysis (TCA) 114
A.3 NUMERICAL EXAMPLES AND DISCUSSIONS 116
A.3.1 Comparing the differences in computational time for FEM and HFEM 116
A.3.2 Result of the static contact analysis of the spur gear 117
A.3.3 Contact analysis of the cylindrical crown gear -- statistics 118
A.4 SUMMARY 119
REFERENCES 145
PUBLICATION LIST 150
VITA 152

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