Statistical investigation of mistuning behaviour of bladed disc systems with ANSYS program

Gas turbine engines are widely used in aviation applications. These engines are quite complex structures consisting of hundreds of stationary and rotary parts. Gas turbine engine bladed discs, are rich dynamical systems that are known to suffer from severe vibration problems. The failures of these bladed discs which are the key components of gas turbine engines not only cause significant economic losses to enterprises and society, but also threaten people's lives. For this reason it is necessary to pass through many analysis and test processes before the designs of gas turbine engines are mature and to avoid possible mistakes. In order to simplify the design process of these highly complex structures and to be able to model the finite elements of the structure all blades on a bladed disc in a gas turbine engies are assumed to be identical. Although the blades are assumed to be identical, the blades are slightly different from each other due to manufacturing tolerances, variations in material properties and wear and tear. In the literature the effects of small variations between blades are known as mistuning. Mistuning coupled with flexibility of the disk, it can localize the vibration energy of the system to a small sector of the disk that containing only a few blades. This phonomena is known as the mode localization. Mode localization often results in a significant increase in the forced response amplitude of a few blades. In consequence of this increasing of a forced response amplitude of a few blades, the high cycle fatigue life of those blades are decreasing. In order to prevent high cycle fatigue failure, researchers must take into account the mistuning behavior of the structure. This mistuning behavior can be divided into two categories to be known mistuning and random mistuning. In known mistuning, the variation of the blades are calculated from the manufactured blades and the high cycle fatigue behaviour calculated for that particular case. However during the operation conditions these blades can be vary from the each other due to the wear and tear. For this reason, blade mistuning is random and can be difficult to measure accurately, making it difficult to predict when localization will occur and what blades will be affected. In traditional methods, the force response amplitude of mistuned blades investigated by using numerical equations that represent the blade behaviour, and statistical methods such as Monte Carlo simulations. In Monte Carlo simulation random sampling is performed to generate mistuning pattern. Obtained results from the random sampling is divited to tuned results and then the amplification factor is calculated. Probability density function and cumulative probability distribution are obtained from these sampling. By the help of probability density function cumulative probability distribution and than 1000 sampling, maximum amplification factor is determined. Today's, although finite element reduction methods are used instead of numerical equations, accuracy of the results vary with the sampling number. In literature review At least 1000 sampling is required for Monte Carlo samples to be able to calculate amplitude factors at 99.9% confidence level. Moreover, Monte Carlo sampling should be done for different standard deviations to find maximum amplification factor. Within the scope of this thesis, 12 bladed academic bladed disc system take into account. Academic bladed disc model was created in ANSYS APDL program parametically. Static analysis was performed under the 10000 RPM. The prestressed effect of the static analysis was reflected in the linear perturbation modal analysis and natural frequencies, mode shapes and harmonic indices were obtained. With the help of these results, harmonic indices versus frequency plot was obtained and frequency veering location were determined. In the light of these information mode superposition harmonic analysis was performed without mistuning strength between the range of 100Hz and 1000Hz. For mode superposition harmonic analysis the structural damping ratio were assumed to 0.05. From the mode superposition harmonic analysis two significant peak points were observed. First peak point was belongs the first modes of the structure and the second peak point was belongs the frequency veering location. The results of the peak points obtained from modal superposition harmonic analysis without mistuning strength are used to calculate the amplification factors. In this thesis, mistuning strength was defined as a normal distribution function and standard deviation for each blade, and face centered central composite design theory was applied instead of Monte Carlo simulations. The standard deviation values 0.01 to 0.1 by using 0.01 increment is investigated with mode superposition harmonic analysis. For each standard deviation value 562 analysis were performed. 5620 analysis were performed to obtain all standard deviation results. For all analysis the outputs were identified as first peak points and second peak points amplification factor. By using these assumption, sampling numbers which is depending on the blade number, are dramatically decreasing. Recall that for each standard deviation, If monte carlo analysis were performed minimum sampling number is 1000. Furthermore this sampling number is not accurate enough to create probability density and cumulative probability distribution. Once design of experiments results were obtained for each standard deviation, the results were used in genetic aggregation response surface methodology to generate response surfaces between inputs and outputs. 10000 random samples were taken for the amplification factors from the response surfaces. By using these sampling points probability density function and cumulative probability distribution were calculated for each standard deviation. Within the help of these functions, %99 confidence level of the two peak points amplification factor were calculated. It has been observed that the maximum amplification factor at the first peak point in the selected standard deviation range 0.01 to 0.1 is increased continuously. Because the first peak point is not at the frequency veering location. The amplification factor has been continuously increased due to the stiffness change in the structure. At the standard deviation of 0.1 the stiffness changes of the structure is ± 28.7%. On the other hand, It has been observed that the maximum amplification factor at the second peak point in the selected standard deviation range 0.01 to 0.1 is not increased continuously. It was observed that the results reached a maximum at the standard deviation value of 0.06. On the other hand, for the standard deviation values 0.01 to 0.06, second peak points amplification factors are greater than first peak points. At the standard deviation of 0.06 the stiffness changes of the structure is ± 18.5%. It is clear to see that at the frequency veering location there is an upper limit of the amplification factor, and this amplification factor occurs at the small mistuning region. Theoretical maximum amplification factor is depending on the number of blade in the bladed disc structure. By using this technique, maximum amplification factor can be determined up to 20 blades. If the structure has more than 20 blades, partial mistuning approach could be used.