# Nonlinear Vibrations of Low Pressure Turbine Bladed Disks: Tests and Simulations
## 2 Experiment  
The experiment was performed on a purposely designed 48-blade scaled TA (Figure 1). The number of blades was defined in order to take into account the room available for the spinning test rig, the possibility to keep the cavity where the UPDs are positioned as close as possible to the original cavity, and, finally, the possibility to easily repeat multiple tests by removing and inserting all the blades and UPDs in a limited amount of time. The scaled bladed disk has been designed from the original one of the AriAS project (144 blades) by preserving the main geometrical features. In particular, the two TA disks supported the same blade and UPD geometry and materials; the same space between adjacent blades at the platform-shank region was preserved, since it is the location where the UPD is inserted; the same Inter-Blade Phase Angle (IBPA) for the excited nodal diameter modes of the original disk was used in order to measure the UPDs' damping effectiveness with the same platform kinematics. Therefore, the ratio between the number of blades of the reference disk and the modified one can be used to scale the nodal diameters under investigation. Specifically, ND8 related to the third modal family used in this work. The term \"third modal family\" refers to a set of natural frequencies where specific nodal diameter (ND) patterns emerge, with ND8 representing the mode with eight nodal diameters. The choice of this mode was motivated by the full-scale 144-blade disk's operational conditions, where it experiences resonance crossing with the ND8 mode during service. This selection allows our scaled model to replicate the relevant dynamic behavior observed in the full-scale disk. ND8 corresponds to the ND24 mode of the reference disk in order to have a common IBPA = 60\({}^{\circ}\).  
Figure 1: (**a**) ARIAS 48-blade disk assembly; (**b**) disk blade unit; (**c**) under-platform dampers. Scaled and re-designed version of 144-bladed disk assembly used in ARIAS project.  
The smaller radius of the scaled test rig did not allow us to keep the same critical rotating speed at which resonance excitation occurs. For this reason, it was decided to firmly press the blade root against the disk slot by means of screws aligned along the radial direction. In this way, the friction damping at the blade root joint is prevented and the measured damping will be associated with the action of the material and UPDs only.  
Post-processing, all the experimental data underwent a forced-response measurement for each blade as well as for critical frequency values by means of the Blade Tip Timing (BTT) system. The BTT system is employed to measure the vibration amplitude of each blade and monitor the disk speed by ensuring the proper positioning of sensors which are placed on the rig casing. Excitation was realized by means of permanent magnets, as in the reference disk, which are mounted on a static flange. Static magnets interact with rotating magnets mounted on the tip of each blade of the rotor.  
Before proceeding with the rotating test, a non-rotating impact test was performed to identify the material damping and the resonant frequency associated with the ND8 mode shape.  
As the next step, the blade is experimentally tested in static and rotating conditions. The experimental spinning rig features two protective cylindrical structures, shown in Figure 2a: an external (component n.2) and an internal one (component n.1). The bladed disk is secured to the rotating shaft within the internal structure using bolts. Two flanges are mounted to the inner ring: the lower flange holds the excitation system based on permanent magnets; the upper flange holds the measurement system based on laser sensors, according to a Blade Tip Timing (BTT) setup.