Dynamics of Cracked Shafts
The problem of cracked rotor dynamics is discussed in Chap. 6. Analytical formulation for crack local flexibility in relation to crack depth yields a supervisory instrument which can give an early crack warning. Fracture mechanics methods provide stress i
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Dynamics of Cracked Shafts
Abstract The problem of cracked rotor dynamics is discussed in Chap. 6. Analytical formulation for crack local flexibility in relation to crack depth yields a supervisory instrument which can give an early crack warning. Fracture mechanics methods provide stress intensity factors for the investigation of rotor’s dynamic performance for varying crack depth. Open cracks lead to linear systems, while closing cracks lead to non-linear ones. Analytical solutions are obtained, which can be used to monitor crack propagation or to identify cracks in service.
6.1 Introduction The behavior of a rotating shaft with a transverse surface crack first attracted attention in the late 1960s in connection with the possibility of crack identification on a large steam turbine where there was a suspicion that one of the rotors had such a crack. Dimarogonas [1] observed the local flexibility of the shaft due to the crack and developed an analytical formulation for the crack local flexibility in relation to the crack depth; he also showed the influence of the crack upon the dynamic response of the rotor. Due to the turbine rotor failures at Southern California Edison’s Mohave station in 1970 and 1971, industry’s attention was focused on problems of turbine-generator shaft failures, caused by transmission system operation and system faults leading to fatigue cracks. Metallurgical examination revealed that the failure was due to fatigue-propagated cracks in the rotors. A sister machine had similar loading history and it was suspect for having the potential for a forthcoming failure of the same type [2].
A. D. Dimarogonas et al., Analytical Methods in Rotor Dynamics, Mechanisms and Machine Science 9, DOI: 10.1007/978-94-007-5905-3_6, Ó Springer Science+Business Media Dordrecht 2013
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6 Dynamics of Cracked Shafts
As a result of Dimarogonas and his colleagues’ efforts, the problem was the subject of a thorough investigation and led to the development of a supervisory instrument which can give an early crack warning. The manufacturer released this instrument for general use in the early 1970s [3]. After 1975 there were a number of publications dealing with this problem [1, 2, 4, 5]. Gash [6] and Henry and Okah-Avae [7] considered the non-linear mechanism of a closing crack with different flexibilities for open and closed cracks. Applying this principle on a De Laval rotor they derived the equations of motion on both the rotating and the stationary coordinate systems, which were solved by an analogue computer. The crack flexibility was determined experimentally. Mayes and Davies [8] performed a detailed analytical and experimental investigation for turbine shafts with cracks. They derived a rough analytical estimate of crack compliance based on Paris energy principle and measured it on a test rig. Although they considered the nonlinear equations for a simple rotor, they obtained analytical solutions by considering an open crack which led to a shaft with dissimilar moments of inertia in two normal directi
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