Calculation of the Forced Response of a Turbine Bladed Disk with Underplatform Dampers
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The study of the dynamic behavior of turbine bladed disks is a topic of great importance. The fluid flowing through the vanes generates an excitation force whose frequency depends on the shaft rotational speed. When the excitation frequency equals the natural frequency of the system, the high vibration amplitude generated can lead to high-cycle fatigue failure. In order to damp vibrations, an effective solution consists in introducing, between the blade platforms, small metal masses called underplatform dampers (UPD). Each damper is pressed against the blade platforms by the centrifugal force: when relative motion takes place at the contacts, the friction forces dissipate vibrational energy. From an industrial point of view, it is fundamental to have effective tools for the design of turbine bladed disks with underplatform dampers. The nonlinear calculation of the bladed disk forced response cannot be computed by the existing commercial finite element codes. As a consequence, numerical tools have been developed in MATLAB at Politecnico di Torino. A first version of a numerical code was developed to calculate the forced response of the Octopus bladed disk equipped with cylindrical underplatform dampers. The Octopus test rig consists of a static blisk with removable blade platforms which allow the introduction of UPDs of different geometry. In this thesis a new procedure is developed to allow extracting from Ansys the mass and stiffness matrices of the disk FE model in cyclic symmetry. As a consequence, it is possible to examine by means of the existing numerical code the whole dynamic of the bladed disk. The code is then enhanced in order to calculate the forced response in a reasonable computational time. Using the analytical calculation of the Jacobian matrices for both the blades and the underplatform dampers, the computational time can be dramatically reduced. This improvement is fundamental because, once the numerical code is validated, it can be used to test underplatform dampers design. The numerical code is eventually validated by comparing the numerical and experimental results.