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

• Main Authors: Yuan-Han Chan, 詹沅翰
• Other Authors: Yan-Shin Shih
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/97078469984330363670

碩士 === 中原大學 === 機械工程研究所 === 97 === 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