含曲線式齒根裂紋之齒輪的疲勞裂紋成長分析

The Analysis of Fatigue Growth of Gear with the Curvilinear Crack at Tooth Root

龔宏仁(Hung-Jen Kuan)

指導教授 ： 施延欣

中原大學/工學院/機械工程研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200549

摘要

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。

關鍵字

齒輪 ； 齒根 ； 曲線式 ； 疲勞裂紋成長 ； 應力強度因子

並列摘要

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.

並列關鍵字

gear ； tooth root ； curvilinear ； fatigue crack growth ； stress intensity factor

參考文獻

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