A comprehensive theoretical, numerical and experimental approach for crack detection in power plant rotating machinery

In order to describe the state-of-the-art on cracked rotor related problems, the current work presents the comprehensive theoretical, numerical and experimental approach adopted by EDF for crack detection in power plant rotating machinery. The work mainly focuses on the theoretical cracked beam model developed in the past years by S. Andrieux and C. Varé and associates both numerical and experimental aspects related to the crack detection problem in either turboset or turbo pump units. The theoretical part consists of the derivation of a lumped cracked beam model from the three-dimensional formulation of the general problem of elasticity with unilateral contact conditions on the crack lips, valid for any shape and number of cracks in the beam section and extended to cracks not located in a cross-section. This leads to the assessment of the cracked beam rigidity as a function of the rotation angle, in case of pure bending load or bending plus shear load. In this way the function can be implemented in a 1D rotordynamics code. An extension of the cracked beam model taking into account the torsion behaviour is also proposed. It is based on the assumption of full adherence between crack lips, when the crack closes, and on an incremental formulation of deformation energy. An experimental validation has been carried out using different cracked samples, both in static and dynamic configurations, considering one or three elliptic cracks in the same cross-section and helix-shaped cracks. Concerning the static configuration, a good agreement between numerical and experimental results is found. It is shown to be equal to 1% maximal gap of the beam deflection. Concerning the dynamical analysis, the main well-known indicator 2× rev. bending vibration component at half critical speed is approximated at maximum by 18% near the crack position. Our experiments also allowed for the observation of the bending and torsion resonance frequency shifts determined by the extra-flexibility induced by the crack in the shaft. The validated crack model is then applied to predict the dynamical behaviour of large industrial rotating machinery and to verify the crack detection capability based on the vibratory response. With respect to 900 MW turboset units, with cracks affecting LP rotors, a map of crack detection capabilities, based on 1× rev. and 2× rev. components as a function of circumferential extension ratio and crack depth, is drawn. If the crack depth is higher than 37% of the rotor diameter, on-line measurements of 2× rev. vibratory level shift allow to detect the crack. On the opposite, 1× rev. monitoring is necessary for cracks with circumferential extension superior to 270°. It is also observed that LP rotor bending mode shift monitoring theoretically allows to detect cracks with depths equal to or greater than 20% of the rotor diameter or with circumferential extension greater than 120°. The difficulties encountered for distinguishing the LP rotor bending mode frequencies, which may also evolve in time, independently from the cracks, limit the industrial application of this latter technique. Therefore new studies will focus on the analysis of torsion dynamic behaviour and on its sensitivity to cracks. With respect to RCP units, when half of the shaft section is cracked, the 2× rev. component remains very small. Whilst the result is simply due to a small excitation, a more accurate estimation of the external forces acting on the shaft could lead to more accurate numerical predictions.