Crack growth analysis and fatigue life estimation in the piston rod of a Kaplan hydro turbine

Abstract

Linear elastic fracture mechanics (LEFM) approaches are seldom used to analyze fatigue problems in hydraulic turbomachinery, where extremely simplified fatigue models are normally considered. In one of the largest Kaplan hydraulic turbines in the world, the piston rod, which is an important load transfer component, was found broken twice at the same location. This event, which leads to extremely high direct reparation costs and indirect costs, is a very useful case for research of fatigue problems in hydraulic turbines by means of LEFM. For this purpose, the crack growth progress in the piston rod is simulated with numerical LEFM techniques. A probabilistic model for the initial flaw size is considered. A reliability criterion, consisting in the probability of not having a critical crack or a fracture in the piston rod after a specific service time, is defined. Based on this model, the influence of initial crack models and operating services of the machine on the reliability of the unit is discussed. The calculated crack path and predicted number of loading cycles as a function of the initial crack size agree with the actual fracture section and operating time to fracture.

Improved damage detection in Pelton turbines using optimized condition indicators and data-driven techniques

“…Machine vibrations in all the monitoring locations were available with the machine in good condition, with incipient damage and with severe damage. 36,37 After that, the machine was repaired and put again into service.…”

New method for determining P‐S‐N curves in terms of equivalent fatigue lives

“…where A, B, and m are the fitting parameters. After the logarithm of both sides for Equation 8, Equation 8 can be expressed into a linear mathematical form. It should been noted in the EQ method that the stress variable can be considered to be (S -A), rather than S, so as to make the fatigue physical properties more visual.…”

“…The TM method consists in an evaluation of the point with a given probability (and confidence limit) at each testing stress level, and then the P ‐ S ‐ N regression is made considering these points. The accurate P ‐ S ‐ N results can be obtained by the TM method only when the sample size is large enough . More importantly, P ‐ S ‐ N curves will be even more costly and more time‐consuming when facing the situation of large‐scatter data, because fatigue failure is sensitive to many factors such as microstructure and defects of materials as well as specimen surface quality .…”

“…The accurate P-S-N results can be obtained by the TM method only when the sample size is large enough. [8][9][10] More importantly, P-S-N curves will be even more costly and more time-consuming when facing the situation of large-Nomenclature: A, B, m, fitting parameters of P-S-N curves; C, confidence level; CV i , coefficient of variation of the logarithmic fatigue life at the ith stress level; ESS, explained sum of squares; EQ, new method for determining P-S-N curves in terms of equivalent fatigue lives; F (), cumulative distribution functions; I, number of testing stress levels; ISO, International Standard Organisation; J i , number of all the experimental life data at the ith stress level; k, one-sided tolerance limit factor; l i , number of the experimental life data used for P-S-N curve fitting at the ith stress level; N, lgN, fatigue lives, and logarithmic fatigue lives; N i,j , fatigue life of the specimen j at the ith stress level; N ω , lgN ω , fatigue lives, and logarithmic fatigue lives of the mixed sample at the baseline stress level; lgN C,R,i , logarithmic fatigue with the confidence level C and survival level R; lg(N C,R,i ) f , lg(N C,R,i ) a , fitted logarithmic fatigue lives, and accurate logarithmic fatigue lives with the confidence level C and survival level R at the ith stress level; Φ, cumulative distribution function of the standard normal distribution; μ i , μ Base , median logarithmic fatigue life at the ith stress level, and at the baseline stress level; R, survival level; RSS, residual sum of squares; S i , stress level with the order of i; TM, traditional method for determining P-S-N curves; σ i , standard deviation of the logarithmic fatigue life at the ith stress level; t, testing time; U, unified coefficient of variation; v, sample size of the mixed sample; w, fatigue life order for the mixed sample; χ, precision level scatter data, [11][12][13] because fatigue failure is sensitive to many factors such as microstructure and defects of materials as well as specimen surface quality. [14][15][16] Therefore, it is of great necessity to propose a new method for determining P-S-N curves, which can save testing time and improve testing efficiency.…”

Operating conditions leading to crack propagation in turbine blades of tidal barrages. Influence of head and operating mode

“…Some researches use the Miner's rule to estimate the relative damage of every operating condition [27][28][29]. Adapted versions of the Paris Law [31,32] have been successfully used to predict the number of cycles to fracture. Finally, the reliability of the machine, defined as the probability of not propagating a crack, has been recently defined by Gagnon et al [33][34][35] using the limits defined by the Kitagawa diagram.…”