PSI - Issue 5

Jaroslav Václavík et al. / Procedia Structural Integrity 5 (2017) 1349–1354 Jaroslav Václavík et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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Shaft cracks usually occur at locations of stress concentration, such as at keyways for shrunk-on couplings and radial holes in generator collector shafts, when torsional loads cause the stresses to exceed the endurance limit of the shaft material. Damage to blades from torsional vibration occurs primarily from resonant response of torsional modes susceptible to excitation from negative sequence current. The blades torsional response frequency can be even shifted due to torsional vibration coupling of the shaft torsional and the LP rotor blade bending modes. Several methods for detecting the blade vibrations have been used in the past: strain gauge tests in operating turbines or non-contacting blade tip timing. The current research involves the use of sensitive torsional vibration strain gauge based sensor. Proximity of gauge locations to large LP blades may enable tracking of blade vibration excursion events. There is also effort to track the changes of blades resonant frequencies from torsional spectra. The torsional natural frequencies of the shaft systems have to be good separated from the frequencies of the induced dynamic impact. It has to be taken in consideration that even small prospective modifications of the rotor have the potential to move the shaft frequencies closer to a resonant condition. This separation represents a frequency band that shaft natural frequencies must be outside of to avoid damaging resonance vibration. These separation frequency bands are provided in ISO Standard (2009). Unit-specific measurements, or in some cases continuous monitoring, eliminates the torsional model uncertainty and permits turbine generator operation in a narrower frequency avoidance window. The objective of this article is to describe the on-line measurement system, which was installed in one of Czech nuclear power stations for continuous monitoring of torsional vibrations of the turbine-generator and to give some results, obtained from more than four years system operations. Torsional vibrations are angular vibrations of an object, typically a shaft along its axis of rotation. As mainly rotational speeds are measured, torsional vibrations are assessed as the variation of rotational speed within a rotation cycle. These RPM variations are typically induced by a non-smooth driving torque or a varying load. Structural sensitive frequencies along a driveline may then amplify and transfer these phenomena leading to comfort, durability or efficiency problems. Two methods based on the shear-stress measurement (direct measurement of the torque) and the twist angle position measurement are available for the torsional vibration investigations. The basic equations between torque M k and angular position α ( t ) and sheer stress τ is coupled with the moment of inertia J z and the radius of the shaft R Most torque sensors are based on the measured shear stress τ at the outer surface of the shaft. The easiest instrumentation is based on the measurement of the relative-angle deformation - the twisting angle Δ α between two separate locations at the distance L on the shaft (1). Using strain gauges, direct measurement of the torsional elongation of shear stress is possible. This system has lower sensitivity to other deformations than torsional. However, exact angular speed and position are not known. Since acceleration is measured, angle and speed can only be derived by integration. It is obvious, that with the system based on torque measurements, the maximum values are detected at nodes of the torsional mode, while with the system based on angular velocity the measurement of the maximum values are detected at antinodes. The torsional vibration using strain gauges is mostly measured with full bridge configuration with four strain gauges T1 to T4, positioned at a 45-degree angle on the shaft, see Fig. 1. The symmetric configuration compensates for unwanted measured quantities such as bending stress. The full bridge is twice sensitive in comparison with half bridge. The full bridge configuration can also be realized with four strain gauges glued only from one side of the shaft and the compensation for the bending stresses is ensured, as well. 2. Systems for measurement of torsional vibrations J z L G J z  z R J  dt d M k          2 2 (1)