PSI - Issue 68

Evgeniia Georgievskaia et al. / Procedia Structural Integrity 68 (2025) 559–565 Evgeniia Georgievskaia / Structural Integrity Procedia 00 (2025) 000–000

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Fig. 1. Characteristic distribution of dynamic stress amplitudes.

In practice, as previously proposed by Georgievskaya (2019), two major groups are available for dividing all loads and stresses: low-frequency and high-frequency ones. For high-capacity hydraulic units rotation frequency f r is usually no more than 5 Hz. Characteristic LF loads are precessions of the vortex core in water passages at part load modes with frequencies (0,2-0,5) f r , rotation frequency vibration f r , doubled 2 f r and tripled 3 f r rotation frequencies, axis vibrations with frequencies of 8-12 Hz. Examples of HF vibrations are: • blade frequency f b = f r ·Z b ( Z b – number of runner blades, Z b = 4-20), • rotor-stator interaction with the frequency f RSI = f r ·Z g ( Z g –guide vanes’ quantity, Z g = 12-40); • Karman vortices of the frequency f К , depending on flow rate and output edge thickness (usually f К = 100-500 Hz). LF loads and stresses are mainly related to transient or hydraulic unit’s non-stable operating modes, for example, working at low and medium part load. LF loads are caused by pressure pulsations in the water passage due to mechanical, hydraulic, electromagnetic imbalances and/or the formation of powerful vortex structures in the water passage that affect the hydraulic unit as a whole. Therefore, LF loads usually have large amplitudes but are active for short periods of time and their frequency of action is not higher than several Hz. Due to their high amplitude, LF loads can cause operational cracks to emerge. However, due to low impact frequencies and short time intervals of impact, LF loads lead to a further stable slow crack growth. Stable crack growth under the action of LF loads alone can continue for decades without causing dangerous damage to HU’s components. HF loads accompany the hydraulic unit’s operation over the entire operating range and cause high-frequency dynamic stresses in its components. These dynamic stresses are related to the excitation of corresponding eigenforms. Amplitudes of these stresses are significantly lower than the amplitude of stresses caused by LF loads (Figure 1). For example, amplitude stress pulsations for the Francis turbine runner on RSI frequency ( f RSI = 40-60 Hz) don’t usually exceed 5% of the static stress value on the same HU operation mode, while the amplitude of LF stresses at medium part load can reach 100-120% of the corresponding average value during the load cycle. Dynamic stress vibration amplitudes caused by Karman’s vortices rarely exceed 0,2-0,3 MPa. SIF at the crack tip calculated according to BS 7910 at HF stress amplitude, is usually below the threshold value which causes crack extension. The lifetime estimation often excludes HF stresses at the design stage which leads to overestimated lifetime forecast and hazardous cracks well before the predicted time of HU components’ failure. 4. Method: concept of “acceptable risk” The proposed actual service-life method estimation of lifetime-determining HU components takes into account the combined LF and HF action. The concept of acceptable risk allows HUs to operate with cracks until they become the most hazardous.