修整型曲線齒輪對齒面接觸應力與負載下傳動誤差之研究

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姓名

駱建成(Chien-Cheng Lo) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

修整型曲線齒輪對齒面接觸應力與負載下傳動誤差之研究
(Characterization of the Modified Curvilinear Gear Set on Tooth Contact Stress and Loaded Transmission Errors)

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摘要(中)

利用直邊飛刀與刀盤創成的曲線齒輪具有高強度、低噪音、潤滑良好且無軸向推力等優點。但有軸向組裝誤差情況時，將會產生不連續的傳動誤差。為避免不連續的傳動誤差，因此本論文所研究之曲線齒輪，將直邊刀具換成圓弧狀刀具再配合刀盤創成曲線齒輪，故稱為修整型曲線齒輪。修整型曲線齒輪嚙合時為點接觸型式，其接觸應力較高可能會影響齒輪的壽命。而傳動誤差的存在已普遍被認為和齒輪嚙合時產生的振動與噪音有密切的關連性。因此如何避免過高的齒面接觸應力與研究嚙合齒輪對所產生負載下傳動誤差為本論文研究之重點。
本論文依據所推導修整型曲線齒輪齒面數學模式，完成齒面接觸分析與曲率分析，並且建立有限元素齒面網格分割電腦程式，透過赫茲應力公式與有限元素分析，探討齒輪刀具參數對齒面接觸應力之影響。
除了以齒面接觸分析探討齒輪未負載之傳動誤差外，本論文整合齒面接觸分析與有限元素分析結果，並且也整合赫茲應力公式所計算彈性變形量與齒面接觸分析整合，依兩者結果研究負載下傳動誤差之情形。

摘要(英)

With several advantages of the classical curvilinear gear generated by straight line fly cutter and cutter disk, it possesses higher bearing and contacting strength、lower noise、better lubrication condition and no axial trust forces characterizations. However, the curvilinear gear set causes discontinuous transmission error in the axial misalignment condition. In this thesis, to prevent discontinuous transmission error, we displaced the he straight line cutter into circular-arc cutter and combined with cutter disk. Thus, it was termed modified curvilinear gear. Under the ideal meshing condition, the contact point of modified curvilinear gear set localized in the middle of the tooth. With the characteristic of parabolic transmission errors, this gear set can also significantly prevent the edge contact and jump transmission errors produced by the horizontal axial-misalignment and vertical axial-misalignment. Therefore, the modified curvilinear gear set indeed processes superiority of transmission.
The mesh of the modified curvilinear gear is bearing contact, so the higher contact stress can affect the life-span of tooth. In addition, the existence of transmission errors has been demonstrated that are closely related to the vibration and noise of gear meshing. Thus, this thesis focuses on how to prevent the overhigh of contact stress and research the mesh gear set that produce loaded transmission errors.
Here, according to the mathematical model of modified curvilinear gear, we analyzed the tooth contact and curvature and developed finite element mesh-generation computer program. Based on the Hertz theory and finite element method, we investigated the effect of tooth contact stress form parameter design of gear cutter.
In addition to investigate the unload transmission errors through tooth contact analysis, and we examined loaded transmission errors which combined with tooth contact analysis and finite element method. Moreover, we also explored the results of elastic deformation calculated from Hertz theory and tooth contact analysis.

關鍵字(中)

★ 負載下傳動誤差
★ 齒面接觸應力
★ 曲線齒輪

關鍵字(英)

★ curvilinear gear
★ tooth contact stress
★ loaded transmission errors

論文目次

摘要 i
Abstract ii
致謝 iv
目錄 v
圖目錄 viii
表目錄 xiii
符號對照表 xiv
第1章緒論 1
1.1 研究背景 1
1.2 文獻回顧 2
1.2.1 曲線齒輪 2
1.2.2 負載下齒面接觸分析 3
1.3 研究目的 4
1.4 論文架構 5
第2章修整型曲線齒輪數學模式 7
2.1 曲線齒輪創成原理 7
2.2 創成修整型曲線小齒輪假想齒條刀數學模式 8
2.3 創成修整型曲線大齒輪假想齒條刀數學模式 11
2.4 修整型曲線小齒輪齒面數學模式 13
2.5 修整型曲線大齒輪齒面數學模式 16
2.6 修整型曲線齒輪齒形特徵 18
2.7 結論 21
第3章齒面接觸分析 22
3.1 傳動誤差分析 23
3.2 傳動誤差範例 26
3.2.1 理想裝配情況 26
3.2.2 組裝誤差 29
3.3 結論 31
第4章曲率分析與赫茲接觸應力 32
4.1 齒面數學模式 34
4.1.1 小齒輪齒面數學模式 34
4.1.2 大齒輪齒面數學模式 34
4.2 曲率分析 35
4.2.1 齒條刀之主軸曲率與主軸方向 35
4.2.2 修整型曲線小齒輪之主軸曲率與主軸方向 37
4.2.3 齒條刀主軸曲率與主軸方向 39
4.2.4 修整型曲線大齒輪之主軸曲率與主軸方向 41
4.3 接觸橢圓與赫茲應力 43
4.3.1 單齒對接觸分析 43
4.3.2 兩齒對接觸分析 46
4.4 接觸橢圓數值範例 52
4.4.1 不同旋轉角度之數值範例 52
4.4.2 改變齒輪刀具參數之接觸橢圓與接觸應力 55
4.5 結論 59
第5章負載下齒面接觸分析 61
5.1 單齒對有限元素模型 64
5.1.1 接觸敏感區域 64
5.1.2 接觸面與表面特性定義 66
5.1.3 邊界條件設定 66
5.2 單齒對模擬結果 67
5.2.1 不同齒輪刀具參數模擬結果 67
5.2.2 接觸橢圓應力分佈 71
5.3 多齒對有限元素模型建立 73
5.4 多齒對模擬結果 74
5.4.1 接觸應力分析 74
5.4.2 齒輪強度分析 78
5.5 負載下傳動誤差 80
5.5.1 有限元素分析計算負載下傳動誤差 81
5.5.2 赫茲應力計算負載下傳動誤差 83
5.5.3 負載下傳動誤差分析範例 83
5.6 結論 87
第6章修整型曲線齒輪製造與接觸齒印實驗 90
6.1 泛用型嚙合測試機 90
6.2 實驗齒輪參數 92
6.3 實驗流程 93
6.4 接觸齒印 94
6.5 結論 97
第7章結論與未來工作 99
7.1 結論 99
7.2 未來工作 101
參考文獻 102

參考文獻

[1] Litvin, F. L., Zhang, J., Handschuh, R. F. and Coy, J. J., “Topology of Modified Helical Gears”, Surface Topography, pp. 41-58., 1989.
[2] Litvin, F. L., Lian, Q. and Kapelevich, A. L. “Asymmetric modified spur gear drives: reduction of noise, localization of contact, simulation of meshing and stress analysis”, Computer methods in applied mechanics and engineering, Vol.188, pp.363-390, 2000.
[3] Litvin, F. L., Vecchiato, D., Gurovich, E., Fuentes, A., Gonzalez-Perez, I., Hayasaka, K. and Yukishima, K. “Computerized developments in design, generation, simulation of meshing, and stress analysis of gear drives”, Meccanica, Vol.40, pp.291-324, 2005.
[4] Litvin, F. L. and Fuentes, A., Gear geometry and applied theory. Cambridge University Press, 2004.
[5] Liu, S. T., “Curvilinear cylindrical gears”, Gear Technology, pp. 8-12, 1988.
[6] Nagata, S., Argia, Y. and Dai, Y., “New method of manufacturing curved tooth trace cylindrical gears using a CNC hobbling machine”, JSME, Vol. 65, no. 630, pp.270-275, 1999.
[7] Dai, Y., Argia, Y., Yanagisawa, A. and Nagata, S., “Study on cylindrical gears with curved tooth traces”, JSME, Vol.66, no.651, pp.187-192, 2000.
[8] Tseng, R. T., Tsay, C. B., “Mathematical model and undercutting of cylindrical gear with curvilinear shaped teeth” Mechanism and Machine Theory, Vol. 34, pp.41-57, 1999.
[9] Tseng, R. T., Tsay, C. B., “Contact characteristics of cylindrical gears with curvilinear shaped teeth ” Mechanism and Machine Theory, Vol. 39, pp.905-919, 2004.
[10] Chen, Y. C. and Gu, M. L., “Finite Element Contact Analysis of a Modified Curvilinear Gear Set” The 26th National Conference on Mechanical Engineering, The Chinese Society of Mechanical Engineers,D17-034, 2009.
[11] Chen, Y. C. and Gu, M. L., “Tooth contact analysis of a curvilinear gear set with modified pinion tooth geometry” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol.225, pp.975-986, 2010.
[12] Vijayakar, S., “A combined surface integral and finite element solution for a three-dimensional contact problem”, Numerical metohdsin engineering, Vol.31, pp.525-545, 1991.
[13] Litvin, F. L., Chen, J. S., Lu, J. and Handschuh, R. F., “Application of Finite Element Analysis for Determination of Load Share, Real Contact Ratio, Precision of Motion, and Stress Analysis”, ASME Journal of Mechanical Design, Vol. 118, p.561-567, 1996.
[14] Zhang, Y. and Fang Z., “Analysis of Tooth Contact and Load Distribution of Helical Gears with Crossed Axes”, Mechanism and Machine Theory, Vol. 34, p.41-57, 1999.
[15] Argyris, J., Fuentes, A. And Litvin, F. L. “Computerized integrated approach for design and stress analysis of spiral bevel gears” Computer methods in applied mechanics and engineering, Vol.191, pp.1057-1095, 2002.
[16] Litvin, F. L., Fuentes, A., Gonzalez-Perez, I., Carnevali, L. and Sep, T. M. “New version of Novikov-Wildhaber helical gears: computerized design, Simulation of meshing and stress analysis.” Computer methods in applied mechanics and engineering, Vol.191, pp.5705-5740, 2002.
[17] Litvin, F. L., Fuentes, A. and Hayasaka, K. “Design, manufacture stress analysis, and experimental tests of low-noise high endurance spiral bevel gears” Mechanism and Machine Theory, Vol. 41, pp.1557-1584, 2006.
[18] Li, S., “Effect of addendum on contact strength, bending strength and basic performance parameters of a pair of spur gears”, Mechanism and Machine Theory, Vol. 43, pp.1557-1584, 2008.
[19] Chen, Y. C. and Tsay, C. B. “Stress Analysis of Helical Gear Set with Localized Bearing Contact” Finite Element in Analysis and Design, Vol.38, pp.707-723, 2002.
[20] Gonzalez-Perez, I., Iserte, J. L. and Fuentes, A. “Implementation of Hertz Theory and Validation of a Finite Element Model for Gear Drives with Localized Bearing Contact”, Mechanism and Machine Theory, Vol. 46, p.765-783, 2011.
[21] Gosselin C., Cloutier L. and Nguyen, Q. D., “A general formulation for the calculation of the load sharing and transmission error underloand of spiral bevel and hypoid gears”, Mechanism and Machine Theory, Vol. 30, No.3, p.433-450, 1995.
[22] Litvin, F. L., Chen, J. S., Lu, J. and Handschuh, R. F., “Application of Finite Element Analysis for Determination of Load Share, Real Contact Ratio, Precision of Motion, and Stress Analysis,” ASME Journal of Mechanical Design, Vol. 118, pp. 561-567., 1996.
[23] Zhang, Y. and Fang Z., “Analysis of transmission errors under load of helical gears with modified tooth surfaces” ASME journal of mechanical design, Vol.119, pp.537-547,1997.
[24] Umeyama, M., Kato, M. and Inoue, K., “Effects of Gear Dimensions and Tooth Surface Modifications on the Loaded Transmission Error of a Helical Gear Pair,” ASME Journal of Mechanical Design, Vol. 120, pp. 119-125., 1998.
[25] Litvin, F. L., Vecchiato, D., Yukishima, K., Fuentes, A., Gonzalez-Perez, I. and Hayasaka, K. “Reduction of noise of loaded and unloaded misaligned gear drives”, Computer methods in applied mechanics and engineering, p.5523-5536, 2006.
[26] Litvin, F. L., Gonzalez-Perez, I., Yukishima, K., Fuentes, A. and Hayasaka, K. “Design, simulation of meshing, and contact stresses for an improved worm gear drive”, Mechanism and Machine Theory, Vol.42, p.940-959,2007.
[27] Wu, S. H. and Tsai, S. J. “Contact stress analysis of skew conical involute gear drives in approximate line contact” Mechanism and Machine Theory, Vol. 44, pp.1658-1676, 2009.
[28] Kolivand, M. and Kahraman A. “A load distribution model for hypoid gears using ease-off topography and shell theory” Mechanism and Machine Theory, Vol. 44, pp.1848-1865, 2009.
[29] 古鳴倫，「具齒形修整之圓弧形曲線齒輪接觸分析」，國立中央大學，碩士論文，民國100年1月。
[30] Johnson, K. L., “One Hundred Years of Hertz Contact” Proceedings of the Institution of Mechanical Engineers Vol.196 No.39 pp.363-378, 1982.
[31] Johnson, K. L., Contact Mechanics, Cambridge University Press, New York, 1985.
[32] Markho, P. H., “Highly Accurate Formulas for Rapid Calculation of the Key Geometrical Parameters of Elliptic Hertzian Contacts” ASME Journal of Mechanical Design, Vol.109 pp.640-647,1987.
[33] Dyson, A., Evans, H. P. and Snidle, R. W., “A simple, accurate method for calculation of stresses and deformations in elliptical Hertzian contacts”, Proceedings of the Institution of Mechanical Engineers, Vol.206 pp.139-141, 1992.
[34] Boresi, A. P. and Sidebottom, O. M., Advanced Mechanics of Materials, 4th Ed. John Wiley and Sons, New York, 1985.
[35] Litvin, F. L., Cgen, N. X. and Chen, J.S., “Computerized determination of Curvature Relations and Contact Ellipse for Conjugate Surface”, Computer methods in applied mechanics and engineering, Vol.125, pp.151-170,1995.
[36] Beyer, W. H., Standard Mathematical Tables, 25th Ed, Boca Raton, Florida, 1979.
[37] Sadd, M.H., Elasticity Theory, Applications, and Numerics, Elsevier Butterworth Heinemann, New York, 2005.
[38] 陳義仁，「受負載之正齒輪對的傳動誤差探討」，國立交通大學，碩士論文，民國94年6月。

指導教授

陳怡呈(Yi-Cheng Chen)

審核日期

2012-8-27

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