·Table of Contents ·Materials Characterization and testing | Non-Destructive Testing of Bulky Centrifugal Fans Conducted for the Purpose of Prolongation of Their Fatigue LifeLADECKI Boguslaw, WOLNY StanislawContact |
Fig1a | Fig1b |
Fig 1: Effective stress field layers s_{H }( MPa ): a - at the bottom rotor surface, b - at the outer surface of blade elements |
Detected cracks* | |||||
Blade number | Operating time [hours] | ||||
2875 | 3498 | 6000 | 7457 | 7671 | |
1 | - | p | t_{3} | t_{4} | t_{4} |
2 | - | - | p | p | p,t_{2},t_{4} |
3 | p | - | - | - | p,t_{2} |
4 | - | - | t_{3} | t_{4} | p |
5 | - | - | - | - | - |
6 | p | t_{1} | - | - | t_{2}, t_{4} |
7 | - | t_{2} | p | p | - |
8 | p | t_{2} | - | - | - |
Table 1: Table 1 Flaw detection results of the rotor no. 42/91 |
The analysis of results presented in Table 1 indicated that, most of the cracks were detected for the weld joining the rotor blade with the cover at the blade entrance (p). In this area, for the examined exploitation time, all together 11 cracks were detected, out of which about half already after 3500 hours of work. The second area considering the intensity of cracks initiations, were welds at supporting cover plates located in the area of blade pressure face near the disc (t_{1}-t_{4}). For that are the number of various types of detected cracks was lower than in the "p" area. In this area the manufactures has applied additional strengthening cover plates, which was difficult to be taken into account in FEM analysis, considering the existing there intensive erosion phenomena. This explains the relatively high number of cracks detected in "t" area in spite of essentially lower value of stresses for this area as computed by FEM.
Micro-and macroscopic analysis of samples cut out of the rotor in Table 1 from areas of fatigue cracks initiations [2] revealed existing defects of welded joints such as lack of the weld penetration in its root and non-metabolic inclusions, which would not be detected under the existing regulations. The spotted defects were the possible place of fatigue cracks initiations.
(1) |
where,e, e_{e}, e_{p} are total, elastic and plastic strains, respectively, E - is the elasticity modulus, K' cyclic strength coefficient and n' - cyclic strain hardening exponent.
The hysteresis loop curve is described as the so called - doubled periodic strain curve [3]:
(2) |
where,De,Ds are ranges of local stresses and strains respectively.
Using the methods applied for low cycle fatigue, the fatigue failure are determined assuming that the durability until the initiation of a crack for elements with a notch under nominal stress DS and nominal strain De, is equal to the total fatigue life of a unnotched specimen under stress range Ds and strain De. In case of constant value of stress or strain amplitude considering asymmetric load for the durability above the transition fatigue life, the fatigue life (N_{f}) may be determined using the formula [3]:
(3) |
were:s_{m} - average stress,
s_{f},e_{f}' - fatigue strength and cyclic ductility strains coefficients, respectively, while
b, c - fatigue strength and cyclic ductility strains exponents.
Local stress and strains in plastically deformed notch area is determined using the Neuber's formula:
(4) |
where the theoretical factora_{k} is replaced by the fatigue of notch factor b_{k }[3].
The fan rotor was made from steel of increased strength 18G2A. For this steel [2] the yield strength was determined at s_{o}=356MPa while the ultimate strength limit at s_{u}=523MPa. This steel in the corrosion state the low cycle properties receive values [4]: K'=843.1MPa, n'=0.131, s_{f}'=872.1MPa, e_{f}'=0.131, b= -0.115, c= -0.716.
FEM calculations confirm the flaw detection examination results, which have found the fatigue cracks in the areas of welded joints, between the blade and cover and disc at its entrance. The highest value of reduced stress in the standard operations conditions s_{H}=365.7MPa, was measured in the place of welded joint between the blade and the cover.
This value was used for fatigue strength evaluation of the rotor, assuming the load of start-up of the device from the state of rest to the maximal value when the nominal rotation reached 6.25 r.p.s., as one stress variance cycle. Because there was no modelling of welded joint geometry (as many surface and internal defects occur) in the FEM calculations, the critical value of notch radius was determined based on an empirical formula: [5]:
(5) |
This value was used when evaluating the notch operating factor based on [3] as:b_{k} = 2, which is substituted to formula (4) to replace a_{k}.
The maximal value of local stress in the notch was found by substitution for e in (4) the right side of formula (1):
(6) |
The range of stress value Ds was determined from a formula resulting from substituting De in (4), by right side of (2) multiplied by 2:
(7) |
Approximate results of formulas (6) and (7) were found numerically using the Newton method. From the calculations the following was determined: s_{max}= 335.8MPa, e_{max} = 7.770×10^{-3}, Ds = 356.4MPa, De= 7.32× 10^{-3}. The calculation method is illustrated in Fig. 2.
Fig 2: Determination of local stress and strain values. |
For such data, by numeric solution of formula (3) using the Newton's method rotor's fatigue life was determined as N_{f} = 192 load cycles.
Given that the fan rotor is exposed to approximately 70 start-up cycles in a year, the determined number of loan cycles until crack initiation, confirms the applied calculation methodology, which points to the low cycle fatigue as the principal cause for crack appearance in the several months perspective.
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