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論文名稱 內嚙合珩磨加工圓柱齒輪與螺桿轉子方法之 研究
(A Study on Internal-Meshing Honing Methods of Cylindrical Gears and Screw Rotors)
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摘要(中) 珩齒(gear honing)是目前齒輪精加工方法之一,已證實可用於改善齒面接觸特性並減少齒輪嚙合噪音及振動。為了掌握及開發珩齒加工之關鍵技術,本論文創新地提出適用於圓柱齒輪與螺桿轉子之內嚙合珩齒加工方法。首先,針對具長齒面螺旋齒輪同時與另外兩個齒輪嚙合之特殊應用,提出一種利用CNC內嚙合珩齒機進行雙導程鼓型齒面修整(dual lead-crowning)之創新方法,通過控制珩磨輪傾角(swivel angle)及珩磨輪轉角,達成在同一長齒面具有兩個導程鼓型修整之圓柱齒輪齒面。其次,更提出應用CNC內嚙合珩齒機進行閉迴路圓柱齒輪齒面拓撲修整之數學模型,通過施予多項式形式之附加運動於珩磨輪傾角、珩磨輪徑向運動及工件齒輪轉角,並建立多項式係數與齒面法向誤差之敏感度矩陣(sensitivity matrix),研究中採用 Levenberg-Marquardt(LM)演算法進行閉迴路疊代計算,以得到最終所需之機台各軸運動方程式,並加工出具有抗扭曲(anti-twisted)、雙鼓型(double-crowned)之圓柱齒輪齒面。最後,提出了一種可用於精磨雙螺桿壓縮機轉子之內嚙合珩齒加工方法,在珩磨過程中,螺桿轉子和珩磨輪間的嚙合類似於一對少齒差、低齒數之交錯軸內嚙合螺旋齒輪,此一創新應用預期具有大幅縮短精磨螺桿加工時間之發展潛力。
摘要(英) Internal-meshing gear honing process is currently one of the economical finishing methods to localize and stabilize the tooth contact pattern and reduce noise and vibration of gear systems. This dissertation proposes novel honing methods for cylindrical gears and screw rotors. For improving the gear contact performance, gears with tooth modification can effectively avoid the edge contact and improve the contact load distribution. The mathematical models are proposed for two novel tooth modification methods of helical gears with internal-meshing gear honing. In the first model, for the special case of a long face-width helical gear meshing with two gears simultaneously, a novel method is proposed for dual lead-crowning for helical gears with long face-widths using a CNC internal gear honing machine. The anti-twist tooth modification is carried out by controlling the swivel angle and the rotation angle of the honing wheel. In the second model, a mathematical procedure is proposed to apply the closed-loop topology modification on helical gears to achieve the double-crowned and anti-twisted tooth flanks on a CNC internal-meshing gear honing machine. Additional motions are added in the radial movement of the honing wheel, the swivel angle of honing wheel and the rotation angle of the work gear in the forms of polynomials. A sensitivity matrix is constructed and Levenberg-Marquardt (LM) algorithm is employed to obtain the polynomial coefficients of additional motions for desired tooth flank topologies. In addition, a novel manufacturing process for screw rotors is proposed using the internal-meshing CNC honing machine. During the honing process, the meshing between the screw rotor and the honing wheel is similar to that for a pair of crossed-axis internal-meshing helical gears with few teeth. This novel application has development potential to significantly reduce the machining time.
關鍵字(中) ★ 珩磨機
★ 齒面修形
★ 雙鼓型修整
★ 齒輪珩磨
★ 螺桿轉子珩磨
關鍵字(英) ★ Honing machine
★ tooth modification
★ double crowning
★ gear honing
★ screw rotor honing
論文目次 摘要 i
Abstract iii
Acknownledgments iv
Table of contents v
List of figures viii
List of tables xi
Nomenclature xii
Chapter 1 Introduction 1
1-1 Research background 1
1-2 Literature review 2
1-3 Research objective 5
1-4 Dissertation overview 7
Chapter 2 Mathematical model for an internal-meshing CNC honing machine 9
2-1 Introduction 9
2-2 Structure and coordinate system of an internal-meshing CNC honing machine 9
Chapter 3 Dual lead-crowning for helical gear with long face width 14
3-1 Introduction 14
3-2 Mathematical model for generation of honing wheel 15
3-3 Methodology of dual lead-crowning of helical gear 19
3-4 Normal deviation of the work gear tooth surface 24
3-5 Numerical examples 26
3-5-1 Modifications of tooth surface by dual lead-crowning for a helical gear 26
3-5-2 Dual lead-crowing for a helical gear with anti-twisted tooth surfaces by gear honing process 29
3-5-3 Tooth contact analysis for the dual lead-crowned tooth surface 31
3-6 Concluding remark 34
Chapter 4 Closed-loop topology modification of helical gears using internal-meshing gear honing 35
4-1 Introduction 35
4-2 Mathematical model for topology modification of cylindrical gears using gear-honing machine 37
4-3 Closed-loop topology modification method for internal-meshing gear honing 42
4-3-1 Numerical solution for machine-axis settings using Levenberg-Marquardt algorithm 42
4-3-2 Closed-loop topology modification 44
4-4 Numerical examples 48
4-4-1 Sensitivity analysis for machine-axis settings in relation to normal deviations of generated tooth surface 48
4-4-2 Comparisons between traditional and the proposed methods for closed-loop topology modification 50
4-4-3 Comparisons of tooth contact performance for traditional and the proposed methods for topology modification 55
4-4-4 Validation of flexibility of the proposed topology modification method 57
4-5 Concluding remark 59
Chapter 5 Mathematical model for screw rotor honing on internal-meshing honing machine 60
5-1 Introduction 60
5-2 Mathematical model for screw rotor honing 61
5-3 Normal errors of screw rotor surface 71
5-4 Numerical examples 72
5-4-1 Verification of mathematical model 72
5-4-2 Influence of additional movements for each machining axis on screw rotor surface 74
5-5 Concluding remark 76
Chapter 6 Conclusions and future work 77
6-1 Conclusions 77
6-2 Future work 78
Appendix 80
References 83
Publications list 89
Author profile 90
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指導教授 吳育仁(Yu-Ren Wu) 審核日期 2020-7-24
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