臺灣博碩士論文加值系統

成型輪磨法包含粗切與精磨兩個加工製程，在現有的齒輪加工方式中為最高精度和最可靠的方法。本論文不僅提出設計多切削刃成型銑刀盤之數學模式以符合不同圓柱齒輪之需求，更提出兩套創新的數值模擬方法分別計算成型砂輪的廓形與模擬成型砂輪的研磨加工，以取代傳統之嚙合方程式計算，同時利用ObjectARX模擬精加工以驗證數值模擬方法能滿足精度需求。本論文內容包括：
1. 依據成型研磨加工的空間幾何關係提出計算成型砂輪廓形的數值方法。此數值方法能替代傳統嚙合條件之複雜計算，而利用所產生的成型砂輪廓形進行成型研磨時不會造成干涉、過切與二次切削的情形。在特殊研磨情況必須加入安裝傾角時，同時提供計算最小傾角的數學模式以求得相符的成型砂輪廓形。
2. 利用AutoCAD為平台作為三微齒輪切削模擬軟體，並使用二次開發軟體ObjectARX與VC++為開發介面。利用布林運算式，提出二微切削模擬方法並與三微切削模擬做比較，以驗證此方法能減少程式運算時間，提高模擬效率。同時也討論成型砂輪設計參數與加工參數對研磨加工所造成的影響。
3. 依據成型研磨加工的空間幾何關係提出二微的成型研磨數值模擬方法。此數值模擬方法能模擬在干涉、過切與二次切削的情況下所得的圓柱齒輪線形以補足傳統嚙合條件只能計算互相嚙合的成型砂輪與圓柱齒輪線形的不足。此數值模擬方法能穩定且有效的減少程式運算時間，同時能計算出在成型砂輪與圓柱齒輪工件上的接觸線。
4. 依據針對捨棄式刀片切削邊緣的等磨耗公式與幾何容許範圍推導出設計成型銑刀本體廓形數學模式。基於等磨耗公式與捨棄式刀片的切削體積來估算刀片壽命以在刀片切削邊緣磨損時更方便維持工件的幾何精度。

Form grinding method has been widely used to manufacture high precision thread on cylindrical workpieces. This thesis proposes a design of form milling cutter with multiple inserts for roughing process and computerized numerical simulation methods instead of simultaneous system equations for finishing process. The research subjects are:
1. Based on the geometrical relations, a geometric approach to determine the grinding wheel profile with or without a tilt angle is presented. Instead of simultaneous system equations, the grinding wheel profile calculated by the proposed method cuts off no extra material even when undercutting occurs.
2. A simplified 2D simulation method executed in AutoCAD ObjectARX CAD software by executing a script file generated by Visual C++ for simulating gear manufacturing process is proposed. The simulation method is demonstrated by taking the cases of manufacturing processes of the cylindrical gear and hypoid gear below with form grinding and face milling processes, respectively.
3. Based on the geometrical relations, this thesis proposes a simplified two-dimensional numerical simulation method for form grinding the thread on cylindrical workpieces without solving the simultaneous system equations that produce numerically unstable solutions in the presence of undercutting, interference, or double enveloping.
4. Based on the equal wear rate for insert cutting edges and the geometrical tolerance, a mathematical model for finding the distribution of cutter body inserts is proposed. The tool life of the insert in every position is estimated based on its cutting material volume and corresponding wear rates for making geometric precision easier to maintain when the insert’s cutting edges become dull.

中文摘要 I
ABSTRACT II
TABLE OF CONTENTS IV
LIST OF FIGURES VII
NOMENCALTURE XIII
NOMENCALTURE XIII
CHAPTER 1 INTRODUCTION 1
1.1 BACKGROUND AND MOTIVATION 1
1.2 LITERATURE REVIEW 3
1.3 THESIS OUTLINES 5
CHAPTER 2 UNDERCUTTING AND INTERFERENCE FOR THREAD FORM GRINDING WITH A TILT ANGLE 7
2.1 INTRODUCTION 7
2.2 GEOMETRIC METHOD TO CALCULATE THE GRINDING WHEEL PROFILE TO AVOID UNDERCUTTING AND SECONDARY ENVELOPING 7
2.2.1 Basic concept of the geometric approach 8
2.2.2 Mathematical Model of the Thread Surface 9
2.2.3 Thread Profiles on the Grinding Wheel’s Transverse Planes 10
2.2.4 A grinding wheel profile that avoids undercutting and secondary cutting 11
2.3 DETERMINATION OF THE MINIMUM TILT ANGLE TO AVOID UNDERCUTTING AND SECONDARY ENVELOPING 13
2.3.1 Profile error of the ground tooth profile 13
2.3.2 Minimum tilt angle to avoid undercutting and secondary enveloping 14
2.4 NUMERICAL EXAMPLES AND DISCUSSIONS 16
2.4.1 Grinding wheel profile that avoids undercutting and secondary cutting 16
2.4.2 Minimum tilt angle that avoids undercutting and secondary enveloping 17
2.5 CONCLUDING REMARKS 18
CHAPTER 3 GENERATING SIMULATION OF 3D GEARS BY USING OBJECTARX 32
3.1 INTRODUCTION 32
3.2 SIMULATION OF OF THE GEAR CUTTING PROCESS 32
3.2.1 Simulation of the form grinding process for cylindrical gears 33
3.2.2 Simulation of the face milling process for hypoid gears 35
3.2.3 Simulated profile error of the generated workpiece surface 39
3.3 NUMERICAL EXAMPLES AND DISCUSSIONS 41
3.3.1 Example 1: Form Grinding for Screw Rotors 41
3.3.2 Example 2: Face Milling Process for a Hypoid Gear 42
3.3.3 Example 3: Undercutting 42
3.4 CONCLUDING REMARKS 44
CHAPTER 4 COMPUTERIZED SIMULATION OF THREAD FORM GRINDING PROCESS 66
4.1 INTRODUCTION 66
4.2 SIMULATION OF THE FORM GRINDING PROCESS 66
4.2.1 Basic simulation concept 67
4.2.2 Mathematical model of the grinding wheel surface 67
4.2.3 Grinding wheel profiles in the equidistant thread transverse planes 68
4.2.4 Approximate ground tooth profile 70
4.3 PROFILE ERROR OF THE APPROXIMATED GROUND TOOTH PROFILE 72
4.4 INSTANTANEOUS CONTACT LINE BETWEEN THE GRINDING WHEEL AND THE GROUND THREAD 73
4.5 NUMERICAL EXAMPLES AND DISCUSSION 74
4.6 CONCLUDING REMARKS 76
CHAPTER 5 DESIGN OF FORM MILLING CUTTERS WITH MULTIPLE INSERTS FOR ROTOR 94
5.1 INTRODUCTION 94
5.2 MATHEMATICAL MODEL FOR THE DESIGN OF FORM MILLING CUTTER BODY 94
5.2.1 Derivation of a standard grinding wheel profile 95
5.2.2 Mathematical model for obtaining the from cutter body profile 97
5.3 MATHEMATICAL MODEL FOR DISTRIBUTING INSERTS ON THE FORM MILLING CUTTER BODY 100
5.3.1 Mathematical model of inserts 100
5.3.2 Mathematical model for arranging inserts onto the axial section profile of form milling cutter body 102
5.4 VARIATION IN THE TOOL LIFE OF EVERY INSERT 104
5.5 NUMERICAL EXAMPLE AND DISCUSSION 107
5.6 CONCLUDING REMARKS 107
CHAPTER 6 CONCLUSIONS AND FUTURE WORKS 128
6.1 CONCLUSIONS 128
6.2 FUTURE WORKS 130
REFERENCES 131
PUBLICATION LIST 134
作者簡介 136

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