Modal Analysis of Mistuned Turbine Blade Packet Due to Combined Blade and Lacing Wire Damage

The turbine disk blade system is a cyclic symmetric structure, initially tuned with all its blades perfectly identical in geometry and material properties; similarly interconnecting lacing wires are of equal stiffness. The cyclic symmetry of the bladed disks gets destroyed due to small differences in material properties or geometric variation between individual blades or lacing wires causing mistuning. Although mistuning is typically small, it can have a drastic effect on the dynamic response of the system. In particular, mistuning can also cause vibration localization for a few blades and the associated concentration of vibration energy can lead to an increase in blade amplitude and stress levels. Numerical simulations are performed with the characteristic equations of the simplified continuum model. Two different damage severity indices are included in the model to study the combined effect of cracked blades and damaged lacing wires on the natural frequencies of grouped blades. This study highlights the characteristic changes in the sub modal frequencies under combined damage in a stand still position. Although the major cause of mistuning is blade damage, lacing wire damage is more frequent and often acts as a precursor to blade damage and thus the present study focuses on mistuning due to combined damage.

Analytical and Numerical Investigation of Lacing Wire Damage Induced Mistuning in Turbine Blade Packet

Investigations of modal parameters for a mistuned packet of turbine blades due to lacing wire damage are reported using analytical and numerical studies with a simplified model. The turbine blade is assumed to be an Euler-Bernoulli beam connected with a lacing wire which is modeled as a mass less linear elastic spring. Thus, the blade is considered as a continuous system and lacing wire as a discrete system. The analytical results using Eigen value analysis are compared with numerical results obtained using commercial finite element package. In real life situation, though not reported in the literature, it is the failure of lacing wire that occurs quite often compared to the turbine blade and acts as precursor to the subsequent blade damage if it goes undetected. Therefore, studying the modal parameters of the grouped turbine blades in the context of lacing wire failure becomes important. The effect of variation of lacing wire location and stiffness indicative of damage resulting in the loss of stiffness on modal parameters is investigated. The study reveals a lot of fundamental understandings pertaining to dynamic behavior of grouped blades compared to the stand-alone blade under the influence of damaged lacing wire.

Influence on Coupling Vibration of Rotor System with Grouped Blades due to Mistuned Lacing Wire

The influence on coupling vibrations among shaft-torsion and blade-bending coupling vibrations of a rotor system with grouped blades was investigated analytically. The natural frequencies and the mode shapes of the system were solved with five- and six-blade cases used as examples. First, numerical results showed how the natural frequencies varied with the wire stiffness and the lacing wire mistuned. The diagrams of the coupling mode shapes were drawn. From the results, it was found that lacing wire did not affect the SB (shaft-blades) coupling modes, but the BB (inter-blades) modes were indeed affected by the lacing wire. At wire stiffness k*=10, the repeated BB modes split into more distinct modes. The BB modes were of (N-1) / 2 and N / 2 multiplicity for odd and even numbered blades. When the system has a mistuned lacing wire, it splits the BB modes and will once more have (N-1) frequencies. In the rotation effect, whatever tuned or mistuned, the lacing wires did not affect the instability. That means the instability preexisted due to rotation and was not induced by lacing wires.

Vibration Localization Analysis of Bladed Disk with Grouped Blades

Vibration localization of bladed disk turns to be much complex when a number of blades are assembled into periodic groups. This work focused on natural frequency distribution and modal localization of bladed disks with grouped blades based on the lumped parameter models, and effects of the blade number in each group on natural frequency were studied. Then Monte Carlo method was applied to analyze the sensitivity of modal localization to the random mistuning of blade stiffness. The results show that the number of blades in each group influences the nature frequency of bladed disk with grouped blades, and modal localization of tuned bladed disk with grouped blades is found in the closely spaced modal region. Moreover, compared to the bladed disk with free blades, the modal localization of bladed disk with grouped blades is much less sensitive to random mistuning of blade stiffness.

A Dynamic Analysis for the Loose Lashing Wire Grouped Blade

The loose lashing wire grouped blade, all blades of which are linked by a loose lashing wire, is a kind of damped blade. The linear analysis method cannot be used for the dynamic analysis of loose lashing wire grouped blade because of the contact between loose lashing wire and blades. A non-linear dynamic analysis method is advanced and an application of the method to a kind of loose lashing wire grouped blade is shown in this paper. First, the nonlinear transient dynamic analysis and maximum entropy spectrum analysis methods for loose lashing wire grouped blade are studied. Then, an algorithm to calculate the dynamical stress of loose lashing wire grouped blade with transient dynamical analysis method is proposed. The proposed method provides a useful numerical calculating method for the calculation of dynamical frequency and dynamical stress of loose lashing wire grouped blades.

Vibrational Response Analysis of Mistuned Bladed Disk System of Grouped Blades

For the purpose of the efficient analysis of a mistuned bladed disk system, a new analysis method which applies the substructure synthesis method and the modal analysis method is proposed. Using the proposed method, the vibrational characteristics of the grouped blades structure are studied. From the results, it is found that the grouped blades structure is very sensitive to the mistuning. It is also found that the mixed grouped blades structure (a bladed disk system consisting of some different types of grouped blades relating to the number of blades contained) has an undesirable effect on the forced response. Moreover, by comparing the vibrational characteristics of the integral shroud blades (ISB) structure with those of the grouped blades structure, it is clarified that the reliability of the ISB structure is superior to other structures also from the viewpoint of the mistuning.