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 and split the eigenvalue pairs. 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, many researchers suggest that mistuning suppresses blade flutter, because the complete traveling wave mode is not formed in a disk. In the previous paper, authors studied the forced response of the mistuned bladed disk, using the reduced order model SNM (Subset of Nominal system Modes), and clarified that the effect of the bladed disk structure on the amplification factor. This work is a follow-up study on the previous paper. The stability analyses of mistuned bladed disks with the free-standing blade structure and the continuous ring-blade structure are carried out extensively, using the reduced order model SNM. Comparing the results of the stability analyses of mistuned bladed disks, the effect of the bladed disk structure on the blade flutter is clarified.
Although bladed disks 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, deviations in the material properties, and wear during operation. These small variations break the cyclic symmetry and split the eigenvalue pairs. Bladed disks with small variations are referred to as a mistuned system. Many researchers suggest that while mistuning has an undesirable effect on the forced response, it has a beneficial (stabilizing) effect on blade flutter (the self-excited vibration). Therefore, it is necessary to optimize a bladed disk for forced vibration and blade flutter. In this study, a practical optimization method of bladed disks that makes resonant stress and amount of unbalance of the bladed disk minimum by sorting the blades on a disk while keeping the stability for blade flutter. To verify the proposed optimization method, first, the original mistuned bladed disk, which has the maximum amplification factor, is generated by Monte Carlo simulations. Second, the optimal bladed disk with the minimum amplification factor and the minimum amount of unbalance is searched by using Monte Carlo simulations and the genetic algorithm. To keep the stability for blade flutter, alternate mistuning is applied. From the analysis results, the validity of the proposed optimization method is verified.
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.
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.
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