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Low cycle fatigue life consumption analysis was carried out in this work. Fatigue cycles accumulation method suitable even if engine is not often shut down was applied together with the modified universal sloped method for estimating fatigue cycles to failure. Damage summation rule was applied to estimate the fatigue damage accumulated over a given period of engine operation. The concept of fatigue factor which indicates how well engine is operated was introduced to make engine life tracking feasible. The developed fatigue life tracking method was incorporated in PYTHIA, Cranfield University in-house software and applied to 8 months of engine operation. The results obtained are similar to those of real engine operation. At a set power level, fatigue life decreases with increase in ambient temperature with the magnitude of decrease greater at higher power levels. The fatigue life tracking methodology developed could serve as a useful tool to engine operators.

The hot section components of gas turbines are prone to failure due to creep [

Knowing that fatigue failure is stochastic in nature [

The basic steps involved in estimating the fatigue life consumption of the gas producer turbine blades are estimation of the maximum stress at the 8 different sections of the blade at each point of engine operation/placing of the maximum stress into blocks, estimation of the cycles to failure corresponding to each block of maximum stresses, carrying out of damage summation to know the damage from the various blocks of stresses.

The blade span is divided into 8 equal sections and the stresses due to centrifugal forces and the bending moment forces are estimated at the 8 different sections of the blade where the maximum value in the 8 sections is used for the fatigue life estimation. The stress model is also similar to that presented in [

σ C , i = F i A c s , i (1)

where A c s , i is the cross-sectional area of the blade at node i , and F i is the centrifugal force at node i .

The bending moment stresses at the base of each section and at the three locations is given by Equation (2),

σ G , i B M = B M X X , i × Y G , i I X X , i + B M Y Y , i × X G , i I Y Y , i (2)

σ G , i B M is the bending moment stress, G stands for L E at the leading edge, T E at the trailing edge and S B at the farthest point in the blade suction surface. I X X and I Y Y are the second moments of areas about the blade axial direction and tangential direction respectively. X G , i and Y G , i are the distances from the centre of gravity to the respective three locations in the axial and tangential directions respectively. The total stress σ G , i T o t at each of the three locations at the base of each section of the blade is,

σ G , i T o t = σ C , i + σ G , i B M (3)

The overall maximum stress σ M a x , i at the base of all the sections considered is used for the life analysis of the blade.

The cycle counting model adopted in this work is that presented in [

N e q = ∑ i = 1 n ( | σ T o t , d i + 1 − σ T o t , d i σ T o t , d S | ) k (4)

where σ T o t , d i , σ T o t , d i + 1 , σ T o t , d S and k are the total stresses at each node for the i ^{th} data point, the next data point, at a set speed level and cycle determining exponent respectively.

The modified universal slopes method [

Δ ε 2 = 0.623 ( σ u E ) 0.832 ( 2 N f ) − 0.09 + 0.0196 ε f 0.155 ( σ u E ) − 0.53 ( 2 N f ) − 0.56 (5)

Δ ε 2 is the total strain amplitude, σ u is the ultimate tensile strength of the

material, E is the Young’s Modulus of the material, ε f is the true fracture ductility, and N f is the number of stress cycles to failure. Equation (5) is expressed in terms of nominal alternating stress amplitude, σ a as,

σ a = 0.623 σ u 0.832 E 0.168 ( 2 N f ) − 0.09 + 0.0196 ε f 0.155 σ u − 0.53 E 1.53 ( 2 N f ) − 0.56 (6)

The stress amplitude σ a is equivalent to the overall maximum stress σ M a x , i obtained from the stress model. The number of stress cycles to failure N f is estimated from Equation (6) using the algorithm presented in

When the number of fatigue cycles at each block of load is estimated and the numbers of cycles to failure corresponding to each block of load are obtained, the cumulative fatigue damage is estimated using damage summation rule given by Equation (6),

D f , i = ∑ i = 1 m N e q , i N f , i (6)

where m is the number of blocks of load formed, N e q , i is the number of cycles corresponding to the i^{th} block, N f , i is the number of cycles to failure corresponding to the stress amplitude at the i^{th} block. D f , i is the fatigue damage parameter which is a fraction of the fatigue life consumed during the period of engine operation. For fatigue failure in practice, the damage parameter varies from 0.8 to 1.2; failure at unity damage parameter is assumed in this work. Thus, at the point of fatigue failure,

∑ i = 1 m D f , i = 1 (7)

The equivalent number of stress cycles could be estimated at any period of engine operation while the cycles to failure for a given block of loads in the given period is estimated using average stress level or the maximum stress in the block to be conservative. In any period of engine operation, the sum of the fatigue damage parameters, D f , s is given by Equation (8),

D f , s = ∑ i = 1 m D f , i = ∑ i = 1 m N ¯ a N f , i (8)

where N ¯ a is the mean value of the equivalent cycles accumulated for the entire period of engine operation, and m is the total number of engine operation

points where fatigue damage parameters are evaluated. If t a = ∑ i = 1 m t i is the time taken to obtain D f , s , the time to fatigue failure at any point of engine operation t f , e q is given as,

t f , e q = ∑ i = 1 m t i ∑ i = 1 m N ¯ a N f , i (9)

In terms of cycles to failure, the relation will be in the form,

N f , e q = ∑ i = 1 m N ¯ a ∑ i = 1 m N ¯ a N f , i (10)

Results of fatigue life analysis are presented in terms of relative fatigue life analysis considered next.

In the low cycle fatigue idealization, obtaining the equivalent number of fatigue cycles to failure at a given period of engine operation and estimating the fatigue damage parameter will only reveal the amount of fatigue life consumed, but this will not tell how well the engine is being operated for the period considered. Like the creep factor approach, if the number of cycles to failure is compared with the cycles to failure at a particular reference point, fatigue life will be obtained relative to the reference point, and this will give the operator of the engine an idea of the wellness of the operation of his engine. The fatigue factor (FF) is given by Equation (11),

FatigueFactor ( F F ) = N f N f , Re f (11)

where N f is the number of cycles to failure at a given engine operation point (corresponding to a particular block of load), and N f , Re f is the number of cycles to failure at the defined reference point. If N f < N f , Re f , the engine is operated at a worse condition with respect to the reference point, if N f > N f , Re f , the engine is operated at a favourable condition with respect to the reference condition. In a given period of engine operation, the equivalent fatigue factor will be estimated. This is the ratio of the equivalent fatigue life (equivalent cycles to fatigue failure) to the cycles to fatigue failure at the reference point; this is given by Equation (12),

E F F = N f , e q N f , Re f (12)

E F F is the equivalent fatigue factor, and N f , e q is the equivalent cycles to failure based on the entire period of engine operation.

The fatigue life algorithm developed in this research is applied to 8 months of engine operation using real engine field data to ascertain the feasibility of blade life tracking process. The LM2500+ engine operated by Manx Utilities at Isle of Man was used as a case study and the power turbine blades were the target.

The equivalent daily fatigue factors in Figures 2(a)-(h) are lower in January, February, March and December of engine operation compared to those obtained in June, July, August and November. This is because fatigue life depends on the stresses on the blades which arise from engine shaft speed and momentum changes. The latter depends on the amount of air intake. In January, February, March and December, lower ambient temperatures were recorded leading to higher air intake and hence higher alternating stress amplitude on the blades. The equivalent fatigue factor for each month of engine operation are thus lower in the months of January, February, March and December as in

At any given power level, increasing the ambient temperature through the range of temperatures considered lead to a decrease in the fatigue factor on the

average. The fatigue factors decrease with ambient temperature because increase in ambient temperature leads to lower mass intake. This is accompanied by lower momentum change stresses and tendency in shaft power level reduction. To keep the shaft power level constant, the engine speed increases leading to increase in centrifugal stresses. The increase in centrifugal stresses is more than the decrease in the momentum change stresses. This leads to reduction in fatigue life. The reduction in fatigue life increases with power level as higher stress amplitudes are experienced at higher power levels. This is shown in

Fatigue life consumption analysis and tracking methodology is developed in this work. The concept of fatigue factor is introduced which tells the wellness of engine operation and makes the engine life tracking feasible. The developed methodology was applied to 8 months of engine operation to track the fatigue life

consumption of the engine for the entire period, and to also test the feasibility of the life tracking process. The fatigue life consumption results obtained for the different months are in line with what is obtainable in real engine operations in many other works―higher fatigue life for lower power level operation and vice-versa. The effect of ambient temperature on fatigue life was investigated at different shaft power levels and two basic observations were made. Fatigue life decreases with increase in ambient temperature at a fixed shaft power level, and the value of the decrease in fatigue life is greater at higher power levels. The set power level is any power level in which the engine operates, say 80% or 900% of engine design power. The fatigue life tracking algorithm developed in this work could be used by engine operators in engine fatigue life consumption monitoring and hence aid them in their decision making pertaining to engine maintenance. Since gas turbine blade failure is hardly due to any single mode of component failure, creep-fatigue interaction failure need to be looked employing same relative life analysis methodology.

This work was supported by The Niger Delta Development Commission (NDDC) Nigeria, and Manx Utilities, Isle of Man, UK.

Saturday, E.G. and Isaiah, T. (2018) Low Cycle Fatigue Life Estimation and Tracking for Industrial Gas Turbine Blades Using Fatigue Factor Approach. Modern Mechanical Engineering, 8, 111-120. https://doi.org/10.4236/mme.2018.82008