Coupled longitudinal and bending vibrations of a rotating shaft with an open crack |
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Affiliation: | 1. Faculty of Engineering, Shahrekord University, Shahrekord, Iran;2. School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China;1. School of Civil Engineering and architecture, Southwest Petroleum University, Chengdu 610500, PR China;2. School of Foreign Languages, Southwest Petroleum University, Chengdu 610500, PR China;3. School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, PR China;4. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, PR China;1. Departamento de Ingeniería Civil, de Materiales y Fabricación, Universidad de Málaga, Escuela de Ingenierías. Spain;2. Departamento de Ingeniería Industrial y Civil, Universidad de Cádiz. Spain |
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Abstract: | The coupling of longitudinal and bending vibrations of a rotating shaft, due to an open transverse surface crack is investigated. The assumption of the open crack leads to a system with behaviour similar to that of a rotor with dissimilar moments of inertia along two perpendicular directions. The local flexibility due to the presence of the crack can be represented by way of a 6×6 matrix for six degrees of freedom in a short shaft element which includes the crack. This matrix has off-diagonal terms which cause coupling along the directions which are indicated by these terms. Here shear is not considered and three degrees of freedom are used: bending in the two main directions and extension. This leads to a 3×3 stiffness matrix with coupling terms. The undamped free and forced coupled vibration are first considered. The coupling is investigated and the effects of unbalance and gravity are examined. Then damped coupled vibration is considered for free and forced vibration. The existence of coupling between longitudinal and bending vibration due to the crack is a very useful property which, together with the sub-critical resonance due to crack, can form a basis for crack identification in rotating shafts. New and interesting phenomena of coupled transverse and longitudinal motion are presented and discussed. |
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