PSI - Issue 22

S.V. Belodedenko et al. / Procedia Structural Integrity 22 (2019) 51–58 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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7

The calculation of the guaranteed lifetime of the shaft casing BF (zone 1, 2) as a monoblock is carried out according to the algorithm for searching the LDF based on the formula (7). In this case, as a variation of the degradation process v D , the variation of the deformation level is v ε = 0,163 . The task was to compare this algorithm with the RSI-method.

Fig.3. Schemes of algorithms for determining the safety indexes of large structures .

The casing of the shaft BF can be divided into elements corresponding to the number of BF coolers. The criticality of their failure is the same and equal to one. To compare both approaches, it is necessary to interpret the parameter of the overloading level in a resource way as c olt = n ol / n Σ . This level can only act on the area of the casing where the cooler does not work. Number of spoiled coolers z ol . Under these preconditions, the RSI models are transformed as follows:

2 lg 10 

 

 

 





ik

ik

lg 10

 

P  

 

 

P LND

ol z

ol z



 .

 ,

(8)

If the parameter c olz is known, then z ol = c olz ∙ z Σ . To use the model β PΣLND in the proposed form is possible subject to some calculation technique. It is more convenient to apply the formula of interdependence: β РΣ = β РΣEXP + 1 . When determining the individual RSI, according to the algorithm for searching the LDF for the deformation fatigue model, v D = 0,11 and c olt = 0,1 were taken. Then for the calculation of elements: c ol =c olt +c olz = 0,1 + (z ol / z Σ ). From the results of calculations of the initial safety index (Fig.4), we can draw the following conclusions . The predicted durability or initial RSI β 0RΣ for a single element Ei is larger than designed for the entire structure E as of monoblock. This is due to the reduced load variation of the element v Di compared to the load variation of the entire structure v D . But when the number of damaged elements increases (more than 15% of coolers - in the present situation), the value of β PΣEXP is sharply reduced (β EXP , Fig.4). Guaranteed lifetime for calculation of the element becomes less than for monoblockal calculation (LDF Σ, F ig.4). This is a consequence of the amalgamating effect of the elements with an exponential reliability function. This effect is leveled if the reliability of the elements changes according to the Lindley law (β LND , Fig.4). You can recommend to determine the upper limit of the guaranteed lifetime of the mechanical system by the model β PΣLND Eq. (8), and the lower limit - by the model β PΣEXP Eq. (8). Or take the RSI as the average level, that is: β РΣ = β РΣEXP + 0,5 . The criticality of the element u i can significantly affect the safety index β ΣP of the system. In series systems, the criticality of the every elements u is → 1. For duplicate elements u ip <1 , i.e. u ip << u is . Due to this, the safety index of