具圓周式裂紋軸的扭轉振動與疲勞裂紋成長分析

Torsional Vibration and Fatigue Crack Growth Analysis of a Shaft with Circumferential Crack

詹沅翰(Yuan-Han Chan)

指導教授 ： 施延欣

中原大學/工學院/機械工程研究所/碩士(2009年)

https://doi.org/10.6840/CYCU.2009.00908

摘要

在本文中，考慮含有圓周式裂紋的懸臂軸，探討其在扭轉振動下的自然頻率及疲勞裂紋成長。利用漢米爾頓原理(Hamilton’s principle)推導統御方程式，將邊界條件帶入後即可得到運動方程式，裂紋軸的勁度是由破壞力學的理論來推導。將運動方程式分離變數法後使用Galerkin的方法整理，再使用四階Runge-Kutta的方法來描述振幅與時間之間的關係。在疲勞裂紋成長的部分是由修正Forman 的模式來計算疲勞裂紋成長與次數的關係。在不同裂紋深度下裂紋對自然頻率和振幅的週期影響以及不同的初始裂紋與初始位移對疲勞裂紋成長的影響，在本文中會逐一討論。 在本文中，在裂紋半徑比aR

關鍵字

軸 ； 扭轉振動 ； 圓周式裂紋 ； 自然頻率 ； 疲勞裂紋成長

並列摘要

In this study that a cantilever shaft with circumferential cracks is considered while discussing natural frequencies and the growth of fatigue cracks under the condition of torsional vibration. Considering natural frequencies, Hamilton’s principle is used to derive government equation, and substitute boundary condition into the government equation so as to get the equation of motion. The strain energy of the equation of motion could get the volume of stiffness while using Paris equation. Separate the variables of motional equation into displacement and time by using the method of variables separation. Then we could simplify motional equation to an ordinary differential equation by the use of Galekin’s method. The relationship between period and time would be determined by using the 4th order Runge-Kutta method. In the other hand, modified Forman model is used to calculate the relationship of fatigue cracks growth and loading cycles of a shaft with a circumferential crack. It is discussed in detail in the following chapters regard to the effect on both natural frequencies and amplitude periods in cracks with different crack depths, and also the effect on the fatigue crack growth in different initial cracks and displacement.
It is found that the natural frequency of this research when aR

並列關鍵字

fatigue crack growth ； natural frequency ； shaft ； torsional vibration ； circumferential crack

參考文獻

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