PSI - Issue 22

234 E. Georgievskaia / Procedia Structural Integrity 22 (2019) 229–234 E. Georgievskaia / Structural Integrity Procedia 00 (2019) 000 – 000  bending vibrations cause different stresses and displacements at identical points of the axisymmetric design: the calculated stresses and displacements differ several times, which is confirmed by the results of experimental data; accordingly, when carrying out strain measurement for adequate determination of the maximum actual stresses in the blade system of the runner, it is necessary to install sensors on all blades;  skew-symmetric bending modes of oscillations lead to linear displacement and the corresponding force reaction on the support nodes and, therefore, can be detected from the data of vibration diagnostics systems; using the above calculation model and the results of field experiments, it is possible to construct a transfer function to determine the magnitude of the dynamic component of stresses on the measured values of vibration displacements;  symmetrical bending modes of vibrations do not cause linear or angular displacements, as well as force or torque reactions in the support nodes due to self-balancing of the structure halves, therefore, in principle, they cannot be detected by diagnostic systems that record the dynamic response only on the supports; to determine the dynamic stresses corresponding to these modes, it is necessary to have additional information on the displacements, for example, the runner hub or the rim; this can be done with sensors that record the gap in the labyrinth seals of the runner between the rotation and stationary parts of the unit;  due to the high rigidity of the runner structure, the appearance of cracks very little effect on changes in the frequency spectrum or vibration amplitudes;  the through crack length of 10% of the total length of the blade joint with the hub corresponds to a frequency deviation only 1-3%;  the eigenvalues spectrum for a single blade lies in the high-frequency region and does not affect the rim and hub;  the presence of a crack on one blade almost does not change the runner frequencies;  under the presence of the cracks on all blades simultaneously, which is unlikely, the deviations in the frequency spectrum will be more noticeable, but will not appear in all modes; such deviations can in principle be recorded by the vibration monitoring system, but the algorithms for processing the data recorded by the system should provide for appropriate procedures to identify signs of crack development. 7. Conclusion Existing diagnostic systems do not allow identifying cracks and, accordingly, not allow to correctly assessing the lifetime of the hydraulic unit or the time of safe operation up to needed repair. The conducted studies show the shortcomings of the existing diagnostic and monitoring systems of hydraulic units from the standpoint of lifetime assessment and make it possible to determine the priority directions of their development for the near future: addition to diagnostic systems with displacement sensors to fix the modes of the runner natural oscillations and refinement of analysis algorithms in order to identify long-term trends eigenvalues spectrum.

References

Frunzăverdel D., Muntean S., Mărginean G., Câmpiani V., Marşavina L., Terzi R., Şerban V. // Failure analysis of a Francis turbine runner. IOP Conf. Series: Earth and Environmental Science – 2010. – № 12(1) – P. 012115. – doi:10.1088/1755-1315/12/1/012115 Nennemann B., Monette C., Chamberland-Lauzon J. // Hydrodynamic damping and stiffness prediction in Francis turbine runners using CFD. IOP Conf. Series: Earth and Environmental Science – 2016. – № 49(7) – P. 072006. – doi:10.1088/1755-1315/49/7/072006 Georgievskaia E. Justification of the hydraulic turbines lifetime from the standpoint of the fracture mechanics. Procedia Structural Integrity. – 2018. – №13. – P.971-975. – doi: 10.1016/j.prostr.2018.12.181