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研究生:龔宏仁
研究生(外文):Hung-Jen Kuan
論文名稱:含曲線式齒根裂紋之齒輪的疲勞裂紋成長分析
論文名稱(外文):The Analysis of Fatigue Growth of Gear with the Curvilinear Crack at Tooth Root
指導教授:施延欣施延欣引用關係
指導教授(外文):Yan-Shin Shih
學位類別:碩士
校院名稱:中原大學
系所名稱:機械工程研究所
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:2002
畢業學年度:90
語文別:英文
論文頁數:53
中文關鍵詞:齒輪齒根曲線式疲勞裂紋成長應力強度因子
外文關鍵詞:geartooth rootcurvilinearfatigue crack growthstress intensity factor
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本研究針對含曲線式裂紋之齒輪嚙合時受到周期性負載作用下,探討疲勞裂紋成長的影響。利用ANSYS建立含裂紋齒輪分析模型,而此研究以有限元素法為基礎分別利用應力強度因子和應變能密度的方法來判斷裂紋成長的方向。方法一,使用利用應力強度因子在裂紋尖端周圍的最大值決定裂紋成長方向;方法二,判斷在裂紋尖端範圍內當應變能密度為最小值時為破裂方向同時可決定延伸之裂紋長度,並且根據Flasker所使用之有限元素法的結果作比較。最後根據ANSYS 5.5所得之應力強度因子KI與有效應力強度因子KIeff利用曲線貼合的數值方法分別得到無因次應力強度因子多項式與無因次有效應力強度因子多項式。在本文中探討齒輪在不同初始裂紋角度並使用應力強度因子KI與有效應力強度因子KIeff針對含裂紋齒輪疲勞壽命作評估,於此依據Flasker所使用之有限元素法與實驗結果做比較。本文亦探討受不同負載頻率作用下對裂紋成長與疲勞壽命之影響。


The fatigue crack growth of gear with curvilinear crack of tooth root under cyclic loading is investigated in this study. AT first, ANSYS model of cracked gear is built up. The stress intensity factor and the direction of crack growth are determined. To determine the direction of crack growth, the predicting crack extension by strain energy density is used to find the minimum strain energy density around of crack tip. The results of crack propagation compared with finite element results by Flasker are provided. Based on ANSYS results of stress intensity factor KI and effective stress intensity factor KIeff of tooth root with curvilinear crack, the dimensionless stress intensity factor KI* and dimensionless effective stress intensity factor KIeff* are determined by curve fitting technique. This study considers different initial crack angles and compares stress intensity factor KI and KIeff for fatigue crack growth with experiment and finite element results by Flasker. The effect of different loading frequency on fatigue crack growth is evident in this study.


中文摘要…………………………………………………………………………i
ABSTRACT………………………………………………………………………ii
誌謝………………………………………………………………………………iii
CONTENTS…………………………………………………………………iv
LIST OF TABLES…………………………………………………………………vi
LIST OF FIGURES………………………………………………………………vii
NOMENCLATURE………………………………………………………………ix
CHAPTER 1. INTRODUCTION…………………………………………………1
CHAPTER 2. PROBLEM DESCRIPTION AND ANALYTICAL PROCEDURES4
2.1 Problem description…………………………………………………………4
2.2 Assumptions …………………………………………………………………4
2.3 Analytical procedures………………………………………………………5
CHAPTER 3. STRESS INTENSITY FACTOR BY ANSYS……………………6
3.1 Finite element method by ANSYS……………………………………6
3.1.1 Element type…………………………………………………………7
3.1.2 Modeling………………………………………………………………7
3.1.3 Crack growth analysis…………………………………………………9
3.2 Strain energy density…………………………………………………………10
3.2.1 Strain energy density formula…………………………………………10
3.2.2 Prediction of crack growth direction……………………………11
3.3 Results and discussion………………………………………………………12
CHAPTER 4. FATIGUE CRACK GROWTH………………………………15
4.1 Modified fatigue crack growth model contains the effect of loading ing frequency…………………………………………………………………15
4.2 Fatigue Crack Growth of Gear………………………………………………15
4.3 Stress Intensity Factor KI and KI eff Effect Service Life…………17
4.4 Service Life of Spur Gear for Various Load Frequencies…………………19
CHAPTER 5. CONCLUSION………………………………………………21
REFERENCES………………………………………………………………22
簡歷………………………………………………………………………………43


1.ISO 6336-3. Calculation of load capacity of spur and helical gear-Part3 Calculation of tooth bending strength, 1996.2.ANSI/AGMA 2101-C95. Fundamental rating factors and calculation methods for involutes spur and helical gears (metric version). American Gear Manufacturers Association, 1995. 3.DIN 3990. Calculation of load capacity of cylindrical gears, 1987.4.P. D. Mcfadden, “Detecting fatigue cracks in gears by amplitude and phase demodulation of the meshing vibration”, Journal of Vibration, Acoustics, Stress and, Reliability in Design., Vol. 108, pp. 165-170, 1986. 5.G. Dalpiaz and U. Meneghetti, “Monitoring fatigue cracks in gears”, NDT & E International., Vol. 11,NO. 1, pp. 149-167, 1997.6.D. Brie, M. Tomczak, H. Oehlmann and A. Richard, “Gear crack detection by adaptive amplitude and phase demodulation”, Mechanical Systems and Signal Processing., Vol. 11, NO. 1, pp. 149-167, 1997.7.V. G. Sfakiotakis, D. E. Katsareas and N. K. Anifantis, “Boundary element analysis of gear teeth fracture”, Engineer Analysis with Boundary Elements., Vol. 20,No. 2, pp. 169-175,1997.8.S. Pehan, T. K. Hellen and J. Flasker, “Applying numerical methods for determining the service life of gears”, Fatigue & Fracture of Engineering Materials & Structures., Vol. 18, No. 9, pp. 971-979, 1995. 9.D. G. Lewicki and R. Ballarini, “Effect of rim thickness on gear crack propagation path”, Transactions of the ASME., Vol. 119, pp.88-95, 1997.10.B. Abersek and J. Flasker, “Stress intensity factor for cracked gear tooth”, Theoretical and Applied Fracture Mechanics., Vol.119, pp. 99-104, 1994. 11.S. R. Daniewicz, J. A. Collins and D. R. Houser, “The stress intensity factor and stiffness for a cracked spur gear tooth”, Journal of Mechanical Design., Vol. 116, pp. 697-700, 1994.12.J. Flasker, S. Glodez and S. Pehan, “Influence of contact area on service life of gears with crack in tooth root”, Communications in Numerical Methods in Engineering., Vol. 11, pp. 49-58, 1995.13.Chung-Hong Yeh, “Effect of Loading on Fatigue Crack Growth of Cracked Gear”, Thesis of Master, Chung Yuan Christian University, 1999.14.P. Paris and F. Erdogan, “A critical analysis of crack propagation laws”, Journal of Basic Engineering, Series D, Vol. 85, pp. 528-534, 1963.15.Michele Ciavarella and Giuseppe Demelio, “Numerical meyhods for the optimization of specific sliding, stress concentration and fatigue life of gear”, International Journal of fatigue, Vol. 21, pp. 465-474, 1999.16.R. W. Landgraf and R. H. Richman, “Fatigue of composite materials”, ASTM STP 569, Philadelphia, pp. 130-144, 1975. 17.A. Blarasin, M. Guagliano and L. Vergani, “Fatigue crack growth prediction in specimens similar to spur gear teeth”, Fatigue and Fracture Engineering Materials & Structures, Vol. 20(8), pp. 1171-1182, 1997.18.R. S. Hyde, G. Krauss and D. K. Matlock, “Phosphorus and carbon segregation. effects on fatigue and fracture of gas-carburized modified 4320 Steel”, Metallurgical and Materials Transactions A” Vol. 25, pp. 1229-1140, 1994. 19.K. Inoue, M. Kato and M. Yamanaka, Fatigue strength and crack growth of carburized and shot peened spur gears, Proceedings of Power Transmission Engineering Conference, ASME, pp.663-668, 1989.20.M. Kato, G. Deng, K. Inoue and N. Takatsu, “Evaluation of the strength of carburized spur gear teeth based on fracture mechanics” ,JSME International Journal, Series C, Vol. 36(2), pp.233-240, 1993. 21.H. F. Bueckner, “Field singularities and related integral representations in Mechanics of Fracture I-Method of Analysis and Solution of crack problem (Edited by G. C. Sih)”, Noordhoff Int. Leyden, 1979. 22.S. K. Gdoutos and R. A. Smith, “Criteria for brittle fracture in biaxial tension” ,Engineering Fracture Mechanics, Vol. 19, No. 5, pp.793-804, 1984.23.G. C. Sih and B. Mcdonald, “Fracture mechanics applied to engineering problem-strain energy density criterion” ,International Journal of Fracture, Vol. 10, No. 3, pp. 305-321, September 1974.24.G. C. Sih, “Strain energy density factor applied to mixed mode crack problem”, Int. Journal of Fracture, Vol. 10, pp. 305-321, 1974. 25.B. Abersek and J. Flasker, “Experimental analysis of propagation of fatigue crack on gear”, Experimental Mechanics, Vol. 3,pp. 226-230, 1998.26.F. Gorner, C. Mattheck and P. Morawietz, “Limitations of the petrosk-achenbach crack opening displacement approximation for the calculation of weight functions”, Eng. Fract. Mech. 22, 269-277, 1985.

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