Periodic Response of Blades Having Three-Dimensional Nonlinear Shroud Constraints

In this paper, a three-dimensional shroud contact model is employed to predict the periodic response of blades having three-dimensional nonlinear shroud constraint. When subjected to periodic excitation, the resulting relative motion at the shroud contact is assumed to be periodic in three-dimensional space. Based on the three-dimensional shroud contact model, analytical criteria are used to determine the transitions between stick, slip, and separation of the contact interface and are used to simulate hysteresis loops of the induced constrained force, when experiencing periodic relative motion. The constrained force can be considered as a feedback force that influences the response of the shrouded blade. By using the multiharmonic balance method along with Fast Fourier Transform, the constrained force can be approximated by a series of harmonic functions so as to predict the periodic response of a shrouded blade. This approach results in a set of nonlinear algebraic equations, which can be solved iteratively to yield the periodic response of blades having three-dimensional nonlinear shroud constraint. In order to validate the proposed approach, the predicted results are compared with those of the direct-time integration method. The resonant frequency shift, the damping effect, and the jump phenomenon due to nonlinear shroud constraint are examined. The implications of the developed solution procedure to the design of shroud contact are also discussed.