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研究生:陳聖文
研究生(外文):Sheng-Wen Chen
論文名稱:具曲線齒形之平行軸圓柱齒輪及錐狀齒輪之設計與分析的研究
論文名稱(外文):On the Design and Analysis of Cylindrical and Conical Gears with Curvilinear Shaped Teeth on Parallel Shafts
指導教授:邱顯堂
指導教授(外文):Shen-Tarng Chiou
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
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:2003
畢業學年度:91
語文別:中文
論文頁數:143
中文關鍵詞:點接觸錐狀齒輪
外文關鍵詞:point contactbacklash
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齒輪在工業上應用甚廣,如汽車變速箱、工具機、減速機及其他多種傳動系統上均可見;其基本功用在使輸入件及輸出件維持一定之轉速比,同時也將扭矩作等比例之放大或縮小。
雖然齒輪之設計與製造技術已有長足的進展,但在某些應用場合,仍有背隙、邊緣接觸及應力過大等問題存在,所以仍有許多專家學者嘗試設計新型齒輪,以期能有更佳的特性。其中,曲線齒形具有點接觸及誤差敏感度低的特性;而錐形齒輪(Conical gear)具有背隙可調整、組裝敏感度誤差低,並可應用於平行軸、交錯軸及直交軸齒輪對的特性。本文之主要目的在以該兩者為基礎,而設計出兼具其優點的新型齒輪。
本文先以具曲線齒型圓柱齒輪為研究主題,並以共軛曲面原理及曲率分析的數學模式為基礎,建立其曲面設計、曲率分析及決定避免過切參數範圍之模式;並作一實例設計與分析,除了其幾何模型的模擬外,也探討其各種特性,並驗證建立之設計與分析模式的正確性。再設計一具曲線齒形錐狀齒輪,其與直齒錐狀齒輪嚙合時,即可兼具點接觸及背隙可調的特性。
本文之研究成果,建立了具曲線齒形圓柱齒輪之避免過切範圍及數學模式,提供設計者一快速判斷過切的依據;並設計一新型齒輪可兼具點接觸及背隙可調的優點,具學術之原創性及實際應用之可行性。
Gear mechanisms have been used extensively in various industrial applications, such as gear boxes on vehicles, machine tools, speed-reducers and various transmission systems. Basically, gears are used to transmit a constant speed ratio between the input and output shafts, and to magnify or reduce the torque with the inverse of the ratio.
Although the technologies for the design and manufacturing of gears have been improved quite a lot in these few decades, however for some applications, the problems of backlash, edge contact and over-stress are still exist. Thus, researches on developing innovative gears with better characteristics are necessary. Among the results of these researches, cylindrical gears with curvilinear shaped teeth have the advantages of point contact in the middle parts of gear surfaces and lower sensitivity due to errors; and conical gears have the advantages of avoiding backlash, ease machining, lower sensitivity due to errors, usability in cases of parallel shafts, intersecting shafts, and skew shafts. The main purpose of this study is to propose an innovative gear pair having good characteristics of both kinds of gears.
Cylindrical gears with curvilinear shaped teeth are the first subject of this study. Based on theory of conjugate surfaces, the models for the surface design and curvature analysis of the gear are developed; consequently, the methodology to determine the ranges of design parameters for avoiding undercutting of the gear is proposed. Furthermore, a conical gear with curvilinear shaped teeth conjugated with a conical involute gear is proposed. The innovative pair of gears have the advantages of point-contact and anti-backlash. Design examples are included, and the models developed are applied to demonstrate various characteristics of the gears, and to verify the correctness of the models developed in this study.
Based on the results of this study, the methodology to determine the ranges of design parameters for avoiding undercutting of the cylindrical gears with curvilinear shaped teeth is proposed, such that the design of this kind of gears can be shorten. It is also shown that the proposed innovative conical gear pair is capable of avoiding edge contact and backlash. Thus, qualified academic papers can be expected to be published, and the proposed gear pair has great potential for various industrial applications.
第一章 前言……………………………………………………………1
第二章 具曲線齒形圓柱齒輪的設計與分析…………………………8
2-1 曲面設計 …………………………………………………………8
2-1-1 坐標轉換矩陣…………………………………………………8
2-1-2 刀具的曲面方程式 …………………………………………14
2-1-3 齒輪的曲面方程式 …………………………………………15
2-2 曲率分析…………………………………………………………19
2-2-1 刀具曲面之曲率分析 ………………………………………19
2-2-2 齒輪曲面之曲率分析 ………………………………………21
2-3 特性分析…………………………………………………………28
2-4 過切分析…………………………………………………………33
2-5 誤差分析…………………………………………………………37
2-6 實例設計與分析…………………………………………………39
2-7 結論………………………………………………………………65
第三章 具曲線齒形圓柱齒輪的特例─正齒輪及螺旋齒輪 ………67
3-1 正齒輪的設計與分析……………………………………………67
3-1-1曲面設計………………………………………………………68
3-1-2特性分析………………………………………………………69
3-1-3實例設計與分析………………………………………………72
3-2 螺旋齒輪的設計與分析…………………………………………82
3-2-1曲面設計………………………………………………………84
3-2-2特性分析………………………………………………………86
3-2-3實例設計與分析………………………………………………90
3-3 結論 ……………………………………………………………100
第四章 錐狀直齒齒輪與具曲線齒形錐狀齒輪的設計與分析……101
4-1 錐狀直齒齒輪的設計與分析 …………………………………101
4-1-1曲面設計 ……………………………………………………103
4-1-2曲率分析 ……………………………………………………105
4-1-3實例設計與分析 ……………………………………………107
4-2 具曲線齒形錐狀齒輪的設計與分析 …………………………109
4-2-1曲面設計 ……………………………………………………115
4-2-2曲率分析 ……………………………………………………119
4-2-3實例設計與分析 ……………………………………………121
4-3 齒印接觸分析 …………………………………………………124
4-4 結論 ……………………………………………………………129
第五章 結論與建議…………………………………………………130
參考文獻………………………………………………………………132
英文摘要………………………………………………………………141
自述……………………………………………………………………143
Barrett, J., 1995, "Conical Helical Gears Control Backlash," Eureka: Engineering Materials and Design, Vol. 15, No. 6, pp. 22-23.
Baxter, M. L., 1948, "Curvature-Acceleration Relations for Plane Cams," ASME Transactions, Vol. 70, pp. 483-489.
Baxter, M. L., 1962, Gear Handbook (Edited by D. W. Dudley), McGraw-Hill, New York, U.S.A., pp. 1.1-1.21.
Brauer, J., 2002, "Analytical Geometry of Straight Conical Involute Gears," Mechanism and Machine Theory, Vol. 37, No. 1, pp. 127-141.
Chang, S.-L., and Tsay, C.-B., 1998, "Computerized Tooth Profile Generation and Undercut Analysis of Noncircular Gears Manufactured with Shaper Cutters," ASME Transactions, Journal of Mechanical Design, Vol. 120, pp. 92-99.
Chen, C.-F., Lin, H.-T., and Tsay, C.-B., 2002, "Mathematical Model and Undercutting Analysis of Modified Helical Gears with Smaller Number of Teeth," Transactions of the Chinese Institute of Engineers, Journal of the Chinese Society of Mechanical Engineers, Vol. 23, No. 4, pp. 301-311.
Chen, C. H., 1979, "Boundary Curve, Singular Solution, Complementary Conjugate Surfaces and Conjugation Analysis in Theory of Conjugate Surface," Proceedings of the 5th World Congress on the Theory of Machines and Mechanisms, Montreal, Canada, pp. 1478-1481.
Chen, C. H., 1981, "A-3 Tooth Form of PK Conjugation - A New Design Concept for Gear Tooth Form," Proceedings of the International Symposium on Gearing and Power Transmissions, Tokyo, Japan, pp. 11-15.
Chen, C.-K., Chiou, S.-T., Fong, Z.-H., Lee, C.-K., and Chen, C.-H., 2001, "Mathematical Model of Curvature Analysis for Conjugate Surfaces with Generalized Motion in Three Dimensions," IMeche, Journal of the Mechanical Engineering Sciences, Vol. 215, pp. 487-502.
Chen, Y.-C., and Tsay, C.-B., 2000, "Tooth Contact Analysis and Kinematic Optimization of a Modified Helical Gear Pair with Involute-Teeth Pinion and Modified-Circular Arc Teeth Gear," Transactions of the Chinese Institute of Engineers, Journal of the Chinese Society of Mechanical Engineers, Vol. 21, No. 6, pp. 537-547.
Chen, Y.-C., and Tsay, C.-B., 2001a, "Mathematical Model and Undercutting Analysis of Modified Circular-Arc Helical Gears," Journal of the Chinese Society of Mechanical Engineers, Transactions of the Chinese Institute of Engineers, Vol. 22, No. 1, pp. 41-51.
Chen, Y.-C., and Tsay, C.-B., 2001b, "Bearing Contact of a Helical Gear Pair with Involute-Teeth Pinion and Modified-Circular Arc Teeth Gear," Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 215, No. 10, p 1175-1187.
Colbourne, J. R., 1987, The Geometry of Involute Gears, Springer-Verlag, New York, U.S.A., pp. 229-238.
Colbourne, J. R., 1989, "The Curvature of Helicoids," Mechanism and Machine Theory, Vol. 24, No. 3, pp. 213-221.
Dai, Y., Ariga, Y., and Nagata, S., 1999, "Study on a Cylindrical Gear with Curved Tooth Traces," Proceedings of the Tenth World Congress on The Theory of Machine and Mechanisms, Finland, pp. 2337-2342.
De Donno, M., and Litvin, F. L., 1999, "Computerized Design, Generation and Simulation of Meshing of a Spiroid Worm-Gear Drive with a Ground Double-Crown Worm," ASME Transactions, Journal of Mechanical Design, Vol. 121, No. 2, pp. 264-273.
Denavit, J., and Hartenberg, R. S., 1955, "A Kinematics Notation for Lower Pair Mechanisms Based on Matrices," ASME Transactions, Journal of Applied Mechanics, Vol. 22, No. 2, pp. 215-221.
Dhande, S. G., Bhadoria, B. S., and Chakraborty, J., 1975, "A Unified Approach to the Analytical Design of Three Dimensional Cam Mechanisms," ASME Transactions, Journal of Engineering for Industry, Vol. 97B, No. 1, pp. 327-333.
Dhande, S. G., and Chakraborty, J., 1976a, "Curvature Analysis of Surface in Higher Pair Contact; Part 1: An Analytical Investigation," ASME Transactions, Journal of Engineering for Industry, Vol. 98, No. 2, pp. 397-402.
Dhande, S. G., and Chakraborty, J., 1976b, "Curvature Analysis of Surface in Higher Pair Contact; Part 2: Application to Spatial Cam Mechanisms," ASME Transactions, Journal of Engineering for Industry, Vol. 98, No. 2, pp. 403-409.
Dhande, S. G., and Chakraborty, J., 1977, Kinematics and Geometry of Planar and Spatial Cam Mechanisms, Wiley Eastern Limited, New Delhi, India.
Dooner, D. B., and Seireg, A. A., 1995, The Kinematic Geometry of Gearing, John Wiley & Sons, New York, U.S.A..
Feng, P.-H., Litvin, F. L., Townsend, D. P., and Handschuh, R. F., 1999, "Determination of Principal Curvatures and Contact Ellipse for Profile Crowned Helical Gears," ASME Transactions, Journal of Mechanical Design, Vol. 121, pp. 107-111.
Fong, Z.-H., and Tsay, C.-B., 1990, "Tooth Contact Analysis of Spiral Bevel Gears," Transactions of the Chinese Institute of Engineers, Journal of the Chinese Society of Mechanical Engineers, Vol. 11, No. 6, pp. 538-544.
Fong, Z.-H., and Tsay, C.-B., 1992, "The Undercutting of Circular-Cut Spiral Bevel Gears," ASME Transactions, Journal of Mechanical Design, Vol. 114, pp. 317-325.
Fong, Z.-H., and Tsay, C.-W., 2000, "Study on the Undercutting of Internal Cycloidal Gear with Small Tooth Difference," Transactions of the Chinese Institute of Engineers, Journal of the Chinese Society of Mechanical Engineers, Vol. 21, No. 4, pp. 359-367.
Gosselin, C., Nonaka, T., Shiono, Y., Kubo, A., and Tatsuno, T., 1998, "Identification of the Machine Settings of Real Hypoid Gear Tooth Surfaces," ASME Transactions, Journal of Mechanical Design, Vol. 120, pp. 429-440.
Hori, K., Hayashi, I., and Iwatsuki N., 1998, "The Ideal Tooth Profiles of Conical-External and -Internal Gears Meshing with Cylindrical-Involute Gears over the Entire Tooth Width," JSME International Journal, Part C, Vol. 41, No. 4, pp. 901-911.
Kang, Y.-H., and Yan, H.-S., 1996, "Curvature Analysis of Variable Pitch Lead Screws with Cylindrical Meshing Elements," Transactions of the Canadian Society for Mechanical Engineering, Vol. 20, No. 2, pp. 139-157.
Kawasaki, K., and Tamura, H., 1997, "Method for Cutting Hypoid Gears (Duplex Spread-Blade Method)," JSME International Journal, Series C, Vol. 40, No. 4, pp. 768-775.
Komatsubara, H., Mitome, K.-I., and Ohmachi, T., 2002, "Development of Concave Conical Gear Used for Marine Transmissions, 1st Report, Principle of Generating Helical Concave Conical Gear," JSME International Journal, Part C, Vol. 45, No. 1, pp. 371-377.
Kin, V., 1990, "Limitation of Worm and Worm Gear Surfaces in Order to Avoid Undercutting," Gear Technology, pp. 30-35.
Lin, C.-Y., Fong, Z.-H., and Tsay, C.-B., 1996, "Tooth Contact Analysis of Hypoid Gears," Transactions of the Chinese Institute of Engineers, Journal of the Chinese Society of Mechanical Engineers, Vol. 17, No. 3, pp. 241-249.
Litvin, F. L., 1968, Theory of Gearing, (in Russian) 2nd ed., Nauka, Moscow, Russian.
Litvin, F. L., 1989, Theory of Gearing, NASA, Washington, D.C., U.S.A..
Litvin, F. L., 1994, Gear Geometry and Applied Theory, PTR Prentice-Hall, Englewood Cliffs, New Jersey, U. S. A..
Litvin, F. L., Fuentes, A., Fan, Q. and Handschuh, R. F., 2002, "Comluter Design, Simulation of Meshing, and Contact and Stress Analysis of Face-Milled Formate Generated Spiral Bevel Gears," Mechanism and Machine Theory, Vol. 37, No. 5, pp. 441-459.
Litivin, F. L., and Gutman, Y., 1981, "Methods of Synthesis and Analysis for Hypoid Gear-Drives of Formate and Helixform," ASME Transactions, Journal of Mechanical Design, Vol. 103, pp. 83-113.
Litvin, F. L., and Krylov, N. N., 1975, "Generation of Tooth Surface by Two-Parameter Enveloping," Mechanism and Machine Theory, Vol. 10, No. 5, pp. 365-373.
Litvin, F. L., Kuan, C., Kieffer, J., Bossler, R., and Handschuh, R. F., 1991, "Straddle Design of Spiral Bevel and Hypiod Pinions and Gears," ASME Transactions, Journal of Mechanical Design, Vol. 113, No. 4, pp. 422-426.
Litvin, F. L., Peng, A., and Wang, A., 1999, "Limitation of Gear Tooth Surfaces by Envelopes to Contact Lines and Edge of Regression," Mechanism and Machine Theory, Vol. 34, pp. 889-902.
Litvin, F. L., Zhang, J., and Handschuh, R. F., 1988a, "Crowned Spur Gears: Methods for Generation and Tooth Contact Analysis─Part 1: Basic Concepts, Generation of the Pinion Tooth Surface by a Plane," Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 110, No. 3, pp. 337-342.
Litvin, F. L., Zhang, J., and Handschuh, R. F., 1988b, "Crowned Spur Gears: Methods for Generation and Tooth Contact Analysis─Part 2: Generation of the Pinion Tooth Surface by a Surface of Revolution," Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 110, No. 3, pp. 343-347.
Liu, C.-C., and Tsay, C.-B., 2002, "Mathematical Model and Contact Simulationsns of Concave Beveloid Gears," ASME Transactions, Journal of Mechanical Design, Vol. 124, pp. 753-760.
Liu, S.-T., 1988, "Curvilinear Cylindrical Gears," Gear Tehnology, Vol. 5, No. 3, pp. 8-12.
Mitome, K.-I., 1983a, "Conical Involute Gear: Part 1, Design and Production System," Bulletin of JSME, Vol. 26, No. 212, pp. 299-305.
Mitome, K.-I., 1983b, "Conical Involute Gear: Part 2, Design and Production System of Involute Pinion-Type Cutter," Bulletin of JSME, Vol. 26, No. 212, pp. 306-312.
Mitome, K.-I., 1985, "Conical Involute Gear: Part 3, Tooth Action of A Pair fo Gears," Bulletin of the JSME, Vol. 28, No. 245, pp. 2757-2764.
Mitome, K.-I., 1991, "Conical Involute Gear, Design of Nonintersecting-Nonparallel-Axis Conical Involute Gear," JSME International Journal, Series 3, Vol. 34, No. 2, pp. 265-270.
Mitome, K.-I., 1993, "Infeed Grinding of Straight Conical Involute Gear," JSME International Journal, Series C, Vol. 36, No. 4, pp. 537-542.
Mitome, K.-I. , 1995, "Design of Miter Conical Involute Gears Based on Tooth Bearing," JSME International Journal, Part C, Vol. 38, No. 2, pp. 307-311.
Mitome, K.-I., and Yamazaki, T., 1996, "Design of Conical Involute Gear Engaged with Profile Shifted Spur Gear on Intersecting Shafts," (In Japanese) Transactions of the Japan Society of Mechanical Engineers, Part C, Vol. 62, No. 598, pp. 2436-2441.
Norton, R. L., 1999, Design of Machinery, 2nd ed., McGraw-Hill, New York, U.S.A., Chap. 8-Chap. 9.
Nutbourne, A. W., and Martin, R. R., 1988, Differential Geometry Applied to Curve and Surface Design, Vol. 1, Ellis Horwood Limited, Chichester, England.
Parametric Technology Corporation, 1997, Pro/Engineer, Version 18, Parametric Technology Corporation, Inc., Waltham, MA 02154, U.S.A..
Raven, F. H., 1959, "Analytical Design of Disk Cams and Three-Dimensional Cams by Independent Position Equations," ASME Transactions, Journal of Applied Mechanics, Vol. 81, pp. 18-24.
Reeve, J., 1995, Cams for Industry, Mechanical Engineering Publications Limited, London, England.
Shtipelman, B. A., 1978, Design and Manufacture of Hypoid Gears, John Wiley and Sons, New York, U. S. A., pp. 148-176.
Struik, D. J., 1988, Lectures on Classical Differential Geometry, Dover Publications, New York, U.S.A..
Takahashi, K., and Ito, N., 1986, "Third-Order Surface Application to Determine the Tooth Contact Pattern of Hypoid Gears," ASME Transactions, Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 108, pp. 263-269.
The MathWorks, 1996, Matlab, the Language of Technical Computing; Using MATLAB, Version 5, The MathWorks, Inc., Maryland, U.S.A..
Tsai, Y.-C., and Jehng, W.-K., 1999, "A Kinematics Parametric Method to Generate New Tooth Profiles of Gear Sets with Skew Axes," Mechanism and Machine Theory, Vol. 34, No. 6, pp. 857-876.
Tsay C.-B., 1988, "Helical Gears with Involute Shaped Teeth: Geometry, Computer Simulation, Tooth Contact Analysis, and Stress Analysis," ASME Transactions, Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 110, NO. 4, pp. 482-491.
Tsay C.-B., Sheu, W.-L., and Wu, C.-H., 1990, "Spur Gears with Crowned Teeth," Transactions of the Chinese Institute of Engineers, Journal of the Chinese Society of Mechanical Engineers, Vol. 11, No. 2, pp. 121-133.
Tseng, R.-T., and Tsay, C.-B., 2001, "Mathematical Model and Undercutting of Cylindrical Gears with Curvilinear Shaped Teeth," Mechanism and Machine Theory, Vol. 36, No. 11-12, pp. 1189-1202.
Wildhaber, E., 1956, "Surface Curvature," Product Engineering, Vol. 27, No. 5, pp. 184-191.
Yan, H.-S., and Chen, H.-H., 1994, "Geometry Design and Machining of Roller Gear Cams with Cylindrical Rollers," Mechanism and Machine Theory, Vol. 29, No. 6, pp. 803-812.
Zhang, Y., and Fang, Z., 1999, "Analysis of Tooth Contact and Load Distribution of Helical Gears with Crossed Axes," Mechanism and Machine Theory, Vol. 34, No. 1, pp. 41-57.
Zhang, Y., and Wu, Z., 1997, "Offset Face Gear Drives: Tooth Geometry and Contact Analysis," ASME Transactions, Journal of Mechanical Design, Vol. 119, No. 1, pp. 114-119.
Zhang, Y., and Xu, H., 2003, "Pitch Cone Design and Avoidance of Contact Envelope and Tooth Undercutting for Conical Worm Gear Drives," ASME Transactions, Journal of Mechanical Design, Vol. 125, No. 1, pp. 169-177.
邱顯堂,陳志弘,1998,”一次包絡曲面曲率分析及其於變導程螺桿機構之應用”,第一屆全國機構與機器設計學術研討會論文集,台南市,台灣,205-212頁。
張益三,黃聖杰,2000,Pro/E入門基礎功能剖析,全華科技圖書股份有限公司,台北市,台灣。
陳志弘,1997,"多重包絡及其應用於變導程螺桿機構的曲面設計之研究",碩士論文, 國立成功大學機械工程學系,台南,台灣。
陳志新,1985,共軛曲面基本原理,科學出版社,北京,中國。
陳朝光,唐余勇,吳宏業,1998,微分幾何及其在機械工程中的應用,哈爾濱工業大學出版社,北京,中國。
蔡錫錚,吳思漢,2002,"平行軸錐形齒輪對齒面寬之最佳設計",第五屆全國機構與機器設計學術研討會論文集,高雄市,台灣,244-250頁。
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