·Home ·Table of Contents ·Materials Characterization and testing

Non-Destructive Testing of Bulky Centrifugal Fans Conducted for the Purpose of Prolongation of Their Fatigue Life LADECKI Boguslaw, WOLNY Stanislaw Contact

1. Introduction

Exploitation of bulky centrifugal fans, which are used mainly in mining and measure 5.35 meters in diameter, causes fatigue cracks in the short time perspective of several thousand hours of work. In spite of earlier conducted activities aimed at an increase of operational reliability of examined elements, it was not possible to extend the period until exchange of an element noticeably. The analysis of magnetic powder inspection results allowed for location of crack initiation areas and propagation directions of the found cracks, which are related to places of local over-rigidity of the construction.
In order to explain the phenomena, rotor strength calculations, using the finite elements method and fatigue analysis, were conducted. The said analysis was a base for modernisation of rotors in centrifugal fans in order to increase their effectiveness and decrease maximum stress values.

2. Strength analysis

Evaluation of fatigue strength of the examined fan rotor requires precise determination of stresses and strains both in the course of standard operation and the transient state.
It is also essential to determine the loading range in the expected time of exploitation. An adequate strength analysis was done based on a numerical model using computer programs of the finite elements method (FEM): FEMAP v-6.01 and CEFEM v-5.0.
Calculation model of the rotor consists of 53608 triangular and quadrilateral elements of the coating type, joint in 50154 nodes. Calculations took into account stresses originating from: inertial forces at standard operations (6.25 r.p.m.), dead weight of the rotor and wind pressure on its blades.
As a result of the calculations, stress and strain fields in the assumed nodes of the model were determined. As an example, layer effective stress field variations are shown in Fig.1 [1], determined in accordance with Huber - Mises (s_H) hypothesis for the rotor and its blades. Dead weight and wind pressure stresses were several times lower than stresses caused by inertia forces, and thus negligible considering their impact on strength and fatigue life of the object. Stresses of maximal values were identified in areas where periodically rotor cracks were found as described in point 3, in particular: at welds joining the blade with the cover at blade entrance (element no. 21391, s_H=365.7MPa) and welds located in the direct vicinity of the blade pressure face near the rotor disk (element no. 16467 - s_H=232.6 MPa ). FEM calculation results were further used in fatigue strength calculations.

Fig1a	Fig1b
Fig 1: Effective stress field layers sH ( MPa ): a - at the bottom rotor surface, b - at the outer surface of blade elements

Projections of fatigue crack initiations and propagation areas in construction elements, has become a part of strength calculations. Fatigue cracks are usually initiated in the notch area, related to geometric discontinuities, in the area of stress accumulation measured by the elastic stress concentration factor a_k.
Since several years theoretical and experimental formulas are applied to both low and high cycle strength. Low fatigue life of elements made of materials of good plastic properties, are connected with the existence of plastic zones in the stress concentration area. In such case, the fatigue life is evaluated using the local strain method.
Then the elastic-plastic strains are the main reason for hysteresis loop appearance. The hysteresis loop area is a measure of scattered energy in the material during one load cycle. Variations of the hysteresis area value existing in each load cycle enable the description of macroscopic changes in the material.
Equation of cyclic strain curve may be determined as the sum of elastic and plastic strains [3]:

(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.

5. Conclusions

The examination results and analysis indicate that, the cause of fatigue cracks initiation in the rotors of bulky centrifugal fans used in Polish mining industry is low cycle fatigue located in the most efforted geometric notch areas usually at welded joints.
An increase of rotor's fatigue life is possible after its modernisation. Change of blade geometry aimed at lowering of stresses in the notch area, together with a adequately designed flaw detection construction control should result in a substantial increase of operating reliability. Actions were already initiated in this year in order to reach this goal.

References:

1. Wolny S., Ladecki B., Cichocinski A., and others: Construction changes of the suction system and the rotor of fan type WPK-5,35 used in the main winding system in mines, for th epurpose of increasing its effectiveness and time of operation. Report no. 5.5.130.593. University of Mining and Metallurgy, Division of Machine Construction and Exploitation. Cracow 1999.
2. Ladecki B., Wolny S., Skowronek T.: Expert Report of fan rotor WPK5.35. Report no. 5.5.130.537. University of Mining and Metallurgy, Division of Machine Construction and Exploitation. Cracow 1999.
3. Dowling N.E.: Mechanical behaviour of materials. Printice Hall. Englewood Cliffs, New Jersey 1993.
4. Kaleta J., Kotowski P.: Influence of accelerated corrosion on strength properties of steel 18G2A. Mechanics. Science Research Papers of Swietokrzyska Polytechnic. Kielce 1995.
5. Ladecki B.: Influence of welded joints geometry defects on their fatigue strength. PhD dissertation. University of Mining and Metallurgy. Cracow 1988.

© AIPnD , created by NDT.net

|Home|    |Top|