No abstract

Although bladed disks are nominally designed to be cyclically symmetric (tuned system), the vibration characteristics of all the blades on a disk are slightly different due to the manufacturing tolerance, deviations in the material properties, and wear during operation. These small variations break the cyclic symmetry. Bladed disks with small variations are referred to as a mistuned system. In the forced response of a mistuned bladed disk, the responses of all the blades become different, and the response of a certain blade may become extremely large due to splitting of the duplicated eigenvalues and distortion of the vibration modes. On the other hand, mistuning suppresses blade flutter, because the complete traveling wave mode is not formed in a disk. Although such mistuning phenomena of bladed disks have been studied since 1980s, almost all studies focused on the amplification factor of the displacement response, and few studies researched the amplification factor of the vibratory stress response. In the previous paper, authors studied the amplification factor expressed by the vibratory stress for bladed disks with the continuous ring-blade structure, using the reduced order model SNM (Subset of Nominal Modes), and pointed out that the amplification factor of the displacement and the vibratory stress is different. This work is a follow-up study on the previous paper. The amplification factor of the vibratory stress for bladed disks with the free-standing blade structure is studied, using the reduced order model SNM. Comparing the mistuning phenomena of bladed disks of the continuous ring-blade structure and the free-standing blade structure, the reason why the amplification factor of the displacement and the vibratory stress is different is clarified.

It is well known that asymmetric vane spacing can result in decreased levels of the excitation at specific frequencies. In the previous paper, the resonant response reduction of mistuned bladed disks due to asymmetric vane spacing was studied by use of the equivalent spring-mass model. Although the mistuned bladed disk should be analyzed by FEA to accurately evaluate the resonant response reduction effect of asymmetric vane spacing, it is unrealistic due to enormous computational time. Therefore, in this study, the mistuned bladed disk is modeled by use of FMM (Fundamental Mistuning Model) to evaluate the resonant response reduction effect of asymmetric vane spacing accurately and practically. First, the frequency response analysis of a simple mistuned bladed disk consisting of flat plate blades is carried out for symmetric vane spacing, using both of FMM and the direct FE model, and the calculated results are compared to confirm the validity of FMM. Second, the frequency response analysis of a realistic bladed disk is carried out for asymmetric vane spacing, using FMM, to examine the effect of resonant response reduction effect.

Although bladed disks of turbomachinery are nominally designed to be cyclically symmetric (tuned system), the vibration characteristics of all blades on a disk are slightly different due to the manufacturing tolerance, the deviation of the material property, the wear during operation, and so on. These small variations break the cyclic symmetry, and split the eigenvalue pairs. The actual bladed disks with the small variations are referred to a mistuned system. Many researchers have studied mistuning, and main conclusions are while mistuning has an undesirable effect on the forced response, it has a beneficial (stabilizing) effect on the blade flutter (the self-excited vibration). Although such mistuning phenomena of bladed disks have been studied since 1980s, almost all studies focused on the amplification factor of the displacement response, and few studies researched the amplification factor of the vibratory stress response. Therefore, in the previous paper, authors studied the amplification factor expressed by the vibratory stress for the lower modes of the bladed disk, using the simple assumption. In this study, the mistuning effect expressed by the vibratory stress for the lower and higher modes are examined, using the reduced order model without any assumptions. First, formulation for evaluating the mistuning effect expressed by the vibratory stress is derived, using the reduced order model SNM (Subset of Nominal Modes). Second, the frequency response analysis of the mistuned simple bladed disk consisting of flat plates is carried out systematically. Finally, comparing the amplification factor of the displacement response with that of the vibratory stress response including the synthesized stress (Mises stress and the principal stress), mistuning phenomena expressed by the vibratory stress are clarified.

Recently, DS (Directionally Solidified) and SC (Single Crystal) alloys have been widely applied for gas turbine blades instead of CC (Conventionally Casting) alloys. The SC blade consists of one columnar grain, and the DS blade consists of several columnar grains of SC, where the growing direction of the columnar crystal is set to the direction of the centrifugal force. The frequency deviation of the DS blade caused by the deviation of the material property seems to become larger than that of the CC blade, because of the number of the independent elastic constants more than the CC blade, the deviation of the elastic constants due to the deviation of the crystal growing direction, and so on. Therefore, the mistuning characteristics of the bladed disk consisting of the DS blades seem to be different from that of the CC blade. In this study, the mistuning analysis of the bladed disk consisting of the DS blades are carried out, considering the deviations of the elastic constants and the crystal angle of the DS blade. The FMM is used to analyze the mistuned bladed disk. The maximum amplitude of the mistuned bladed disk of the DS blade is estimated by the Monte Carlo simulation combining with the response surface method, and the calculated results are compared with those of the CC blades.