The paper describes work that has been carried out into the flexural vibrational behavior of a rotor mounted on several bearings and containing a transverse crack. A method of solving the equations of motion of a general system is presented. This method utilizes standard rotor dynamics computer programs and enables calculations on large systems to be made on a routine basis. An approximate method of estimating the reduction of a section diameter required to model a crack for use in beam theory based on finite elements is given which is simple to use and gives acceptable results in practice. The application of the methods to some large turbogenerators is described.
The effects of a transverse crack on the dynamics of a multi-rotor, multi-bearing system have been studied experimentally using a spin rig. It is concluded that except for very large cracks, the vibrational behavior is similar to that of a slotted shaft with additional excitation due to the crack opening and closing. It confirms the theory, described elsewhere, that it is possible to calculate the behavior of a cracked and/or slotted rotor for a realistic turbogenerator model for crack depths sufficient to give a measurable vibration vector change. The dynamic stresses in the cracked shaft were also measured. The results show how the dynamic bending moment at the crack tip depends on the speed of rotation of the shaft and the crack depth. The results are compared with a theoretical treatment previously reported and good agreement obtained. It is concluded that for crack depths in excess of one third the way through, the shaft the dynamic bending moment must be used for fracture mechanics calculations.
A study is presented of the symmetrical steady‐state motion of a rigid shaft supported by two ‘short’ (Ocvirk) journal bearings. The equations of motion for a balanced or unbalanced shaft were solved using numerical ‘initial value problem’ techniques. Frequency analysis, which was used to determine the components of the steady‐state motion, confirmed that, for most conditions, the motion was asymptotically periodic comprising a small number of components—principally at synchronous and half synchronous frequency. However, a region of the operating space was found, in which the motion was complex and did not settle to a limit cycle. An estimate of the extent of this region is given and the suspected cause investigated.
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