ケーシング内で回転するロッドの危険速度に関する理論的研究

海洋ボーリングロッドの危険回転速度 (第3報)

抄録

Theoretical method has been developed for analysing the critical speed of a rod rotating in a flexible casing in case of an off-shore boring. Then, the critical numbers of revolution of the rod in practical cases have been calculated. and the results have indicated the useful guides for the design and operation of the off-shoreboring.
The main guides obtained are as follows:(1) There are two kinds of the critical numbers of revolution of the rod, one of which is caused by the in-phase mode of the coupled lateral vibration of the rod and casing, and the other by the out-of-phase mode of the vibration.
(2) The critical number of revolution of the rod pertaining to the in-phase mode becomes higher in case of a larger value of the diameter-ratio which is defined as the ratio of the outer radius of the casing to that of the rod. Furthermore, the rate of rise of this critical number is greater in case of a higher mode of the critical speed. On the other hand, as the diameter-ratio increases, the critical number of revolution of the rod pertaining to the out-of-phase mode first rises and then approaches to a constant value.
(3) An increase of the span-length of the rod, which is equal to the depth of the water, causes the critical numberof revolution of the rod to be lowered, but it does not affect the above-mentioned phenomena.
(4) The critical number of revolution of the rod rises as the tensile load axially applied at the top of the rod increases. However, the rate of rise of the critical number is greater within the range of a smaller diameter-ratio in case of the in-phase mode of vibration. In case of the out-of-phase mode, however, the rate is greater in the range of a larger diameter-ratio.
(5) The increasing tensile load axially applied at the top of the casing leads to a little rise of the critical number of revolution of the rod pertaining to the in-phase mode of vibration and it causes a slight rise of the critical number pertaining to the out-of-phase mode only in the range of a smaller diameter-ratio.
(6) As the ratio of the Young's modulus of the casing to that of the rod increases, the critical number of revolution of the rod pertaining to the in-phase mode rises, especially in the ratio larger than 1.0 but the critical number pertaining to the out-of-phase mode tends to approach a constant value.