Thermal Effects Due to Vibration of Shafts
Chapter 8 deals with the inverse problem of the one encountered in Chap. 5, e.g. the heat generated by torsional vibration of rotating shafts. The corresponding mechanisms are associated with internal damping and plastic deformation. Practically all the e
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Thermal Effects Due to Vibration of Shafts
Abstract Chapter 8 deals with the inverse problem of the one encountered in Chap. 5, e.g. the heat generated by torsional vibration of rotating shafts. The corresponding mechanisms are associated with internal damping and plastic deformation. Practically all the energy of 476 plastic deformation is transformed into heat. For elastic deformation part of the strain energy is transformed into heat, depending on material loss factor. This phenomenon has been identified as the cause of large-scale failures of power equipment, with electrical disturbances being the cause of rotor torsional vibration. Maximum temperatures given in the form of design nomograms can assist in estimating the overheating of shaft of rotating machinery, where such phenomena are present. A typical turbo-generator shaft is analyzed for vibrations occurring during electrical transients.
8.1 Heat Propagation Due to Torsional Vibration of Shafts Torsional vibrations of shafts result in heat generation due to material damping. In some cases, temperatures can reach high values affecting the reliability of machine members. Such a case was reported for the generator exciter shaft failures at the Southern California Edison. Mohave Station [1, 2], due to torsional vibration resulting from subsynchronous resonance or the electromechanical system. The heat generated produced high temperatures which destroyed the exciter insulation and accelerated shaft failure. This chapter gives a quantitative account of the temperatures generated in the shaft and over its surface because of torsional vibration. The heat is generated due to material damping and, for plastic deformation, due to plastic flow.
A. D. Dimarogonas et al., Analytical Methods in Rotor Dynamics, Mechanisms and Machine Science 9, DOI: 10.1007/978-94-007-5905-3_8, Ó Springer Science+Business Media Dordrecht 2013
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8 Thermal Effects Due to Vibration of Shafts
Dynamic effects due to surface friction heating have been reported for rotating shafts [3–5, 7–12], Extensive studies were also reported on the effect of material damping on the vibration response of shafts [12–17]. Barenblatt et al. [18]. studied heat propagation caused by a crack in a vibrating elastic solid due to material damping. Panteliou and Dimarogonas [19–21] reported on the temperatures produced during torsional vibration of rotating shafts. A uniform shaft is supposed to undergo forced torsional vibration. In general, vibration of this sort can have a linear mode between nodes for lumped mass systems, and a harmonic mode for continuous shafts. Therefore, the torsional vibration amplitude will be [3] ul ¼ az cos xt uc ¼ Cl cos
pz cos xt L
ð8:1Þ ð8:2Þ
where z is coordinate along shaft axis, and subscripts l and c mean lumped mass and continuous system, respectively. L is mode length and a and Cl, are vibration amplitude parameters. The energy of elastic deformation for unit volume under shear stress s will be s2 w¼ ð8:3Þ 2G but 1 s ¼ GDH 2 where H = du/dz, D is shaft diameter (D
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