一般傳動機械如:汽車、機車...等，主要動力來源都是以齒輪傳動為主，本文是探討機車傳動的齒輪，齒輪傳動會因為齒型設計不當、裝配誤差、結構共振、加工精度...等，都可能產生傳動元件的噪音，除了以上的因素齒輪的齒形參數也扮演著極重要的角色，不一樣的參數變化也會影響到齒輪的傳動。
本論文研究內容是齒形幾何參數改變對於傳動穩定度及接觸應力的影響，藉著CAD(Computer Aided Design)電腦輔助設計軟體 Solidworks 建立齒輪模型，在將其模型匯入CAE(Computer Aided Engineering)電腦輔助分析軟體 ANSYS進行暫態分析(transient dynamic analysis)，分析完的結果在匯出經由Matlab來做後端訊號處理，並且利用以傅立葉轉換(Fourier Transform)為基礎的快速傅立葉轉換(Fast Fourier Transform) 做為分析方法，然後針對暫態分析中的作用力來進行時域(time domain) 、頻域(frequency domain) 來做分析及比較，再來判別不同的齒形幾何參數，對於齒輪的齒根應力、傳動穩定上有甚麼影響。最後可以歸納出齒形參數改變的影響，提供一個齒形設計上的分析檢驗流程。

For general transmission machinery such as cars, motorcycles etc., the main power sources are all generated through transmission of gears. In this paper, the gear of the transmission of a motorcycle is explored. Due to several reasons, for example: improper tooth type design, error of assembly, structural resonance, and machining in accuracy, the transmission gears may produce noise. Also, the gear parameters play important roles of the gear transmission.

The focus of this research is the effects of gear geometric parameter on transmission stability and contact stress. By using the CAD (Computer Aided Design) software called Solidworks, gears are modeled. Then the models are imported into CAE (Computer Aided Engineering) software ANSYS to analyze transient dynamic analysis. The results of the analysis are exported to Matlab to do the digital signal process. Finally, the responses of the system are frequency analyzed and also are analyzed in time domain. It is found out that the influence of contact stress and transmission stability is strongly influenced by the gear parameter. It is concluded that a gear design analysis process has been developed by changing the gear design parameter.

[1] F.L. Livitn and A. Fuentes, Gear Geometry and Applied Theory, Cambridge University Press , New York, 2004.
[2] J. Brauer, A general finite element model of involute gears,Finite Elements in Analysis and Design, Vol.40, pp. 1857-1872, 2004.
[3] C.B. Tsay, “Helical Gears with Involute Shaped Teeth: Geometry, Computer Simulation, Tooth Contact Analysis, and Stress Analysis Trans,” ASME, J. Mech. Transm. Autom. Des. 110 (4), pp. 482-491, 1988
[4] Y. C. Chen, C.B. Tsay, “Stress analysis of a helical gear set with localized bearing contact,” Finite Elements in Analysis and Design 38 pp. 707-723, 2002
[5] D.L. Logan, A First Course in the Finite Element Method. Second edition, Bostion: PWS-KENT, 1992.
[6] K. J. Huang and T. S. Liu, “Dynamic analysis of a spur gear by the dynamic stiffness method,” Journal of Sound and Vibration, Vol. 234, pp.311-329, 2000
[7] C. Hung, “Integration of finite element analysis and optimum design on gear systems,” Finite Elements in Analysis and Design, Vol. 38, pp. 179-192, 2002
[8] J. Brauer, A general finite element model of involute gears, Finite Element Anal. Des.40, pp. 1857-1872, 2004
[9] K. Y. Yoon and S. S. Rao, “Dynamic load analysis of spur gears using a new tooth profile,” ASME Journal of Mechanical Design, Vol. 118, pp. 1-6, 1996
[10] C. B. Tsay and Z. H. Fong, The mathematical model of Wildhaber-Novikv Gears Applicable to Finite Element Stress Analysis, Mathematical and Computer Modeling, Vol. 12, No. 8, pp. 939-946, 1989
[11] 李輝煌，ANSYS 工程分析基礎與觀念，高立圖書有限公司，2005年
[12] 劉晉其&褚晴暉，有限元素分析與ANSYS的工程應用，滄海書局，2006年
[13] J.E. Shigley, C.R. Mischke, Mechanical Engineering Design. 5th edition, New York: McGraw-Hill, 1989.
[14] Hertz, H., On the contact of elastic bodies, J. reine und angew Math, Vol. 92, 56-57, 1897
[15] Hertz H, On the contact of rigid elastic solids, and on hardness. Miscellaneous papers. Macmillian, London, 1986
[16] K.L. Johnson, Contact Mechanics, UK: Cambridge University Press, 1985.
[17] N. Chandrasekaran, W. E. Haisler, R. E. Goforth, "Finite Element Analysis of Hertz Contact Problem with Friction", Finite Elements in Analysis and Design, Vol. 3, pp. 39-56, 1987

[18] ANSYS, Inc., ANSYS 7.0 HTML Online Documentation. ANSYS Tutorials. Chapter 8: Contact Tutorial. USA:SAS IP,Inc.,2003.
[19] C.T Wang, Applied Elasticity. New York : McGraw-Hill , 1953.
[20] ANSYS, Inc., Structural Nonlinearities - ANSYS Rev. 5.5. USA: SAS IP, Inc., 1998.
[21] MSC.Software Co., MSC.MARC Vol. A: Theory and User Information. USA: MSC.Software Co., 2000.
[22] ANSYS, Inc., ANSYS 7.0 HTML Online Documentation. Structural Analysis Guide. Transient Dynamic Analysis. USA: SAS IP, Inc., 2003.
[23] ANSYS, Inc., Dynamics - Training Manual. ANSYS Release 6.0 USA: SAS IP, Inc., 2002
[24] P.Kohnke,ANSYS Theory Reference - Release 5.6. USA: SAS IP, Inc., 1999.
[25] K. Aslantas ,S. Tasgetiren , A study of spur gear pitting formation and life prediction ,wear 257,1167-1175, 2004
[26] 王如鈺，“齒輪原理概要”，KHK齒輪叢書，民國82年6月
[27] George H. Martin,機動學(機構學)(第二版)，高立圖書有限公司，1994年
[28] R.W Clough, The finite element method in plane stress analysis. Proceedings of American Society of Civil Engineers,2nd Conference on Electronic Computation ,Pittsburgh , PA,pp. 345-378, Sep. 1960.
[29] A. Hrennikoff ,Solution of problems in easticity by the frame work method. ASME Journal of Applied Mechanics, Vol. 8, No. 4, pp. 169-175, 1941.
[30] M.J Turner ,E.H. Dill, H.C. Martin and R.T. Melosh , Large deflections of structures subjected to heating and external loads. Journal of Aeronautical Sciences, Vol. 27, No. 2,pp. 97-107,1960.
[31] T.R Chandrupatla and A.D Belegundu, Introduction to finite ELements in Engineering. USA: Prentice-Hall,1991.
[32] 陳清松，螺旋齒輪及相體有限元素分析及實驗，國立成功大學機械工程學系碩士論文，九十三年六月。
[33] 吳柏賢，聲音全像法於傳動系統噪音之分析，國立成功大學系統及船舶機電工研究所碩士論文，九十五年七月。
[34] 林益呈，靜音鏈傳動系統之聲場模擬分析，國立成功大學系統及船舶機電工程學研究所，碩士論文，2009
[35] 李仁傑，鈸型結構壓店患能氣之聲場模擬分析與實作，國立成功大學系統及船舶機電工程研究所，碩士論文，2009
[36] R.D. Cook, D.S. Malkus and M.E. Plesha, Concepts and Applications of Finite Elemnet Analysis. Third edition, New York: John Wiley & Sons, 1989.

[37] Tsay C.-B., Sheu, W.-L., and Wu, C.-H, "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, 1990
[38] Mehmet TOPAKCI, H. Kursat CELIK, Deniz YILMAZ, Ibrahim AKINCI, 'Stress Analysis on Transmission Gears of a Rotary Tiller Using Finite Element Method,' AKDENİZ ÜNİVERSİTESİ ZİRAAT FAKÜLTESİ DERGİSİ, 21(2), 155–160, 2008
[39] ANSYS, Inc., ANSYS 7.0 HTML Online Documentation. Structural Analysis Guide. Transient Dynamic Analysis. USA: SAS IP, Inc., 2003
[40] K.J. Bathe, Finite Element Procedures. USA: Prentice-Hall, 1996
[41] Timoshenko S. & Goodier J. N., 'Theory of Elasticity',3rd Edn. New York, London, McGraw-Hill,1951